SHE'S PROUD of her household budget book, he's a multimillionaire. She entered politics because a rattling manhole cover sent her enraged to City Hall; he, for the more tra- ditional reasons of public service -- "to whom much is given, very much is expected." She's the daughter of an immigrant from Hungary, and a Jew; he's the grandson of the founder of Ralston-Purina, and an Episcopal priest. She says he's "running scared"; he counters that "I always campaign like a man possessed."

Missouri has rarely seen such an odd couple of candidates. Harriett Woods, the only Democratic woman nominated for the United States Senate, is among the few women on the national level to envelope-stuff her way up the political ladder from the suburban middle class. She's running hard against Republican John C. Danforth, the incumbent with several trust funds and a 900-acre farm near the town of Flat.

So hard, in fact, that she's just closed the large gap between them. This morning, the St. Louis Globe-Democrat is to publish a poll reporting that Woods and Danforth are now even, each with 47 percent of the vote.

Woods has an earnest midwestern approach. "Hi! I'm Harriett Woods and I'm running for Senate!" she says. Danforth campaigns with an almost religious intensity. "We, as Christian men and women, have a special obligation," he told clergymen in St. Louis last week. Then he climbed into a six-seat Beechcraft and flew to Missouri's Bootheel, hitting a steakhouse, a grain elevator, a Republican pep talk, a laundromat. "I truly believe I'm going to win," he says. "But I'm not sure, and I never am."

The next day dawned as Woods drove north along the Mississippi River toward Mark Twain country, stopping at a picnic, a barbecue, an apple festival and, in an old house in Hannibal, a wine-and-cheese fund-raiser where they put on the lace tablecloth and brought out the silver.

"Lots of luck, dear," said one Hannibal supporter afterward, slipping a $350 check into her hand. "Girls can do everything."

The World Series may be consuming Missouri's attention, but this Senate race makes for fine watching as well. Danforth, 46, a Republican moderate sometimes mentioned as a future vice president, is still ahead in money, raising $1.75 million to Woods' $750,000. He says that none is from his own checkbook, although $36,000 did come from a collection of 18 Danforth cousins, uncles, siblings and his wife. He's also well-known in a state where his television ads seem nearly as frequent as those of Atari.

Woods, 55, was an upset winner in the August primary, running without the support of her party. A liberal state senator from University City, she has the backing of the Missouri State Labor Council (Danforth has the Teamsters'), and the endorsement of the St. Louis Post-Dispatch. Although fre- quently called a "city girl," she did well in the primary in the rural areas that Missourians call "outstate."

There seems a sense of siege in the Danforth campaign; aides are openly nervous about the sudden interest of reporters anticipating a possible kill or at least some good scratches. "Frankly, we're sort of sick of the national press swarming into Missouri to cover Harriett Woods," complains Carrie Francke, Danforth's campaign manager. John Powell, the Republican state chairman, is calling Woods "Missouri's own George McGovern" because of her "pro-choice" abortion stand and her support for the ERA, and adds that she has those "long-haired, nutty environmentalists in her corner." Christopher Bond, the Republican governor, has told Danforth to get tough. Danforth will only say that she's a "nice lady."

But Missouri, the traditionally Democratic state that elected Harry Truman, Stuart Symington and Tom Eagleton, is suffering a 9 percent unemployment rate, small-business failures and layoffs from factories. Danforth supports President Reagan's economic program; Woods is strongly against it. Democrats hope the recession will trigger an upset. Woods reminds people ceaselessly that "were it not for a tragic accident, my opponent wouldn't be here"--referring to the primary night six years ago when Jerry Litton, the popular Democratic congressman whom Danforth would have run against, was killed in a plane crash. She's also not above saying that Danforth represents "that kind of patrician, do-good-but-we'll-make-the-decisions-and-really-keep-the-power approach to American society."

Her background is that of the local activist who joined the League of Women Voters and licked stamps for the party. A gangly former television producer with a talent for speaking in 30-second sound bites, she is serious and sensible, the good student who always got A's. She has neither Millicent Fenwick's eccentricity nor Nancy Kassebaum's money. But she's one of an increasing number of women entering politics from the broad base of average America--and is politically deft at using that, too. "I know what it's like to pay utility bills and raise three sons," she tells crowd after crowd.

This election, as they say in Missouri, gives you a choice--between your preacher or your mother. The Political Pace

7:30 a.m: Woods and her aide, Mark Hurley, are speeding toward coffee and doughnuts with the Democrats in Bowling Green. Really speeding. A patrolman pulls them over and gives a ticket to Hurley, who's 22 years old and mortified. "That's all right, Mark," Woods says, patting his arm maternally. "I'll pay for it." By 8:45, she's telling 35 people in the Bowling Green community center that "I can't tell you how thrilled I am that I am standing here as the Democratic nominee for United States senator. Little did I think, years and years ago, when I was licking envelopes for Stuart Symington . . ."

Woods, a tall woman with a head of bushy, slightly graying hair, was born Harriett Friedman in Cleveland (she's a distant relation of Sen. Howard M. Metzenbaum D-Ohio ), but grew up on the south shore of Chicago. By that time her father had become a successful advertising salesman; her mother was a nationally ranked tennis player. "There's no doubt I come from a line of very strong women," she says. "My grandmother, my mother, we all want to be achievers. We want to be--the best."

After graduating from the University of Michigan, she worked as a reporter at the St. Louis Globe-Democrat, where she married a colleague, Jim. She raised her three children, went back to work as a television producer, was elected to the City Council and, in 1976, to the Missouri State Senate, where she got attention for trying to improve nursing home standards. She knew nothing about political campaigns when she first ran, so she had gone to the local women's political caucus for help. "One of them lent me her file box, and another lent me her campaign manager," she says. "And that's how I started."

1 p.m. She has marched in the Applefest parade in Clarksville, a hamlet tucked into the rolling hills along the Mississippi River; met merchants in the nearby town of Louisiana; had another pastry and a cup of coffee; and given an interview to KPCR, "Cowpasture Radio." Now she's eating chili at a picnic in Hannibal. "You heard that Reagan's going to the Moon next week?" says Joe Haynes, the fireman who's dishing it out. "He heard there's two men working--and he's going to lay one of them off." Other Democrats in the Mississippi River counties north of St. Louis, even those who had voted for Reagan, said similar things. Martha Clark, whose husband was laid off recently when a Hannibal yearbook publisher folded, put it this way: "I won't vote for him again. I admired him as an actor--but I think he's doing some acting now."

It has turned into a beautiful fall day in Hannibal. Mayor John Lyng, a Woods partisan who has watched the local business failures of Beatty Jewelry, the Huck Finn Theater, Beek Builders and Kee T.V., talks under the sycamore trees. "The difference between Danforth and most people in Missouri is this: Danforth has never been in the position where he knows where the money runs out," he says. "His support, if he has a credible opponent, is very soft. There aren't a lot of people who hate him, but there aren't a lot of people who love him, either."

5 p.m: "Running for the U.S. Senate was the most difficult decision--outside of family ones--that I've ever made," says Woods, who's just been to a barbecue, a senior citizen's high-rise and a small fund-raiser. The hills of Rte. 36 pass by in the dwindling sunlight. "I had already started doing all this stuff when they let me know, in no uncertain terms, that someone else was going to be the nominee, someone who could raise money, someone who would be more acceptable to the rural areas, and wouldn't I like to be secretary of state? At which point I said, 'Don't talk to me about any kind of secretary.' I was in effect being told that if you do this, you're going to ruin your political career . . . but you have to take risks, and if you aren't willing to do that occasionally, then there's no hope. So we started out."

She's gone from home most of the time. Her husband, now a retired Post-Dispatch editor, plays golf and fends for himself. "Sure, Jim blows up sometimes," she says. "Because it's hard. But he's been very good. He's expanded. He now can cook more than a hamburger. He's got a whole repertoire of dishes . . . . Sure, some days the staff knows not to call him, if I'm out on the road and I didn't let him know where I was. Sometimes he feels left out, just like the wives of male candidates."

"I thoroughly approve of what she's doing," says her husband. "Oh, it gets vexing occasionally, of course. I had a bad summer. We had ice damage on the roof, and then it leaked in this summer and ruined the plaster, the wallpaper and the paint. Then the tile around the shower sprung a leak. I had to take care of all the repairs--and she normally does all of that. But she was supportive of me all those years. I couldn't do anything else."

5:45 p.m. Barell House Pizza, Monroe City. Woods is complaining about possible cuts in social security benefits to a small crowd of Democrats. The air conditioner's too loud, and people ignore her. Then a couple walks by, the man leading a partially blind and crippled wife. Woods asks if they'd like a seat. No, says the couple, just the bathroom. Woods continues, but on the couple's way out, in the middle of her complaints about social security, the man breaks in. "That's right," says the man, Fred Wake of Detroit. "Just because we got married, they took away my wife's social security." He leads his limping wife away. There's an awkward silence and then Woods, inspired, begins to almost shout. Everybody listens.

Back in the car, she says she has "mixed feelings" about being a "woman politician," but is certainly using the attention -- if not the money -- it gets her. "A woman isn't networked into the establishment," she says, "one where somebody picks up the phone and says, 'Tom, listen, how about giving me some money for good old Joe? You know good old Joe, he comes from the Lion's Club . . . Suddenly, the men are saying after I call -- 'Harriett?' " The Public Servant

9 a.m. Danforth begins in St. Louis, speaking to a meeting of the Missouri press association, just hours after the announcement of the 10.1 percent national unemployment rate. "I'm not down in the dumps," he says afterward. "Everybody knows we're in the soup. How we get out of the soup is the issue." He thinks Reagan's economic program is the "necessary approach"; at more than a dozen stops throughout the day, he blames the Democrats for the mess. "I do not believe it is possible to bring the economy to its feet," he says, "by repeating the same policies that brought it to its knees."

11:30 a.m. He's been interviewed at the Post-Dispatch, an almost consistently liberal newspaper, and says afterward that there's "no chance" of an endorsement--"although I don't think they think I'm sleazy or anything." With 20 minutes to kill before lunch, he decides to give his two traveling reporters a tour of the neighborhood around Lindell Boulevard where one of his grandmothers lived. The car winds past stone houses that look like tiny versions of European castles.

Danforth, a beak-nosed Princeton graduate who likes to listen to Jimmy Buffett on a Sony Walkman while he jogs, is worth as much as $7 million. Although he and his three siblings have little to do with the company his grandfather founded and his father ran, they are still among the largest single shareholders. In 1981, Danforth's reported income from investments was close to $450,000. He hates it when people refer to his political motivation as "noblesse oblige." "That's a stuffy, fuddy-duddy expression," he says, at the same time admitting that public service "was certainly ingrained in me as a child."

He graduated from Princeton, entered Yale's divinity school and got a law degree there as well. He practiced law in New York, went back to Missouri, was elected state attorney general in 1968, then U.S. senator in 1976. His six years on Capitol Hill have been marked, in the words of the Post-Dispatch, by "limited success" -- principally in curbing auto imports to the United States. He hasn't alienated many Missourians, although he's famous back home for complaining about imports while he wears Italian-made Guccis. He is regularly described as aloof, which bothers his wife. "They've always said that," says Sally Danforth from their home in Northwest Washington. "It's weird. Like the press always uses that word S-C-I-O-N. I don't even know how to pronounce it. I think what that means is snob."

Asked if she ever is ready to blow up when her husband is campaigning and has forgotten to call home to tell her where he is, Sally Danforth responds, carefully: "Don't push my button." When they were married 25 years ago, she didn't know he'd go into politics. "Whatever makes him happy makes me happy," she says, adding that "I didn't encourage him to do it, and I haven't exactly been behind him, pushing and clapping. I just sort of accept it." She says she "has raised five children in 15 years pretty much by myself, and they're all good kids--no druggies, no alkies, no dropouts. . . . Obviously, the campaign gets to you, but after it's over, I'm going to have a husband. So it could be worse."

Danforth himself isn't particularly introspective about politics. "Why do I enjoy it?" he says. "I don't know. That's my life. It's kind of 'into the fray.' And I've never felt that I wanted to do it forever." On the Tuesdays that he's in Washington, he administers communion at the St. Albans parish church.

Noon. He speaks to Clergy for Life, giving a tepid anti-abortion speech: "The chances of winning the battle get dimmer and dimmer as the years go on," he says. "But does that mean your role is over?" He tells them to worry about world hunger and nuclear war, gets into his car, stops at his mother's place in Clayton to pick up some clean shirts. "Will I have time to shave?" he asks Carrie Francke plaintively, then goes over the night's schedule, which includes a high school football game that coincides with the St. Louis Cardinals and Atlanta Braves playoff game. "I'm watching a high school football game during the playoffs?" he asks.

4 p.m. He's been to the grain company in Cape Girardeau, the Republican pep talk, a newspaper interview and the laundromat. Now he's in a van, heading for the airport. "I think she should be very proud of her campaign," he says of Woods. "So far." When the governor told a reporter that he felt Danforth should step up his campaign, Danforth says that "words cannot describe my reaction." He insists he's campaigning hard because "it's a small period of time and I don't want to get sacked." He will neither attack Woods nor respond to any of her personal comments about him. "Am I so desperate to win an election that I'm sick about the whole thing at the end of it?" he says. "Gosh. We've had so many negative campaigns. And what you don't want is to hype the campaign for your opponent, on a national scale, beyond all reason."

Back on the plane, another aide, Craig Kilby, tells him a talk with some girl scouts has been added to his evening schedule. "Why do we have to do the girl scouts," says Danforth, "when there's a playoff game?" Playing Hard

It's 1 a.m., and Woods is heading back to St. Louis after an 18-hour day. She's had dinner in a high school cafeteria with the Lewis County Democrats, appeared as the keynote speaker at their gala and now, as the reporter is falling asleep, she is still talking. She tells favorite stories from the Missouri Senate, like the time a colleague screamed "That broad!" at her. "I thought it was the high point of my life in the Senate," she says. "I had driven him crazy." She also talks about the loneliness. "Outside of some friends Jim and I have seen for years," she says, "I really don't have anyone close . . . in the Senate, you can't just say, 'Let's go get a hamburger tonight.' It's hard to do that with the guys."

By the end of his day, Danforth has spoken at the Grecian Steak House in Kennett ("Now serving fresh farm-raised catfish" says the outdoor sign), given a radio interview, and is working the crowd at the football game. Craig Kilby is loaded up with campaign leaflets. "Are we going to pass out literature?" says Danforth. "I don't think we should. I think that's gauche." Danforth's in a much better mood since the playoff game has been called because of rain, which means he won't miss it. "Now I can relax," he says.

Several days later, when the Cardinals are in the World Series, he explains why he's running so hard. "You take the ballgame last night," he says. "The score was 10 to nothing. I'm not ahead 10 to nothing. But you didn't see the Milwaukee Brewers be lackadaisical the last inning of that game. They played hard."

He ended his day at the football game in Kennett by going to the home of some supporters for a drink--but not before taking note of what time Woods planned to begin campaigning the next day.

"7 a.m.?" he said. "Tell her she's starting too early."