The hardboiled conservative men who run the Republican Party in this rural outpost on the edge of "Little Dixie" are casting their lot this November with a woman who campaigns for Congress from a pink van.

To hear them talk, House candidate Carrie Francke is a combination of Harry S. Truman, who grew up 100 miles away, Wonder Woman and the Girl Next Door. By hard work, they say, she has gone a long way toward dispelling the notion that "northeast Missouri isn't ready for a woman anything."

"This isn't any ordinary woman, she's tough and aggressive," gushed Kirksville Mayor Russell D. Roberts, a veteran of political wars. "She doesn't have any foolish ideas."

Francke, 30, has a solid shot at winning. But she may be an exception.

The experts had expected 1984 to be the year of the woman in American politics, a time of dramatic breakthrough, symbolized by Geraldine A. Ferraro and her history-making role as the Democratic vice-presidential nominee. But with the election less than a month away, it appears that women -- hampered by underfinanced campaigns and, in some cases, unusually tough scrutiny -- will make only modest gains in races for the House, traditionally a launching pad for higher office.

Republican and Democratic Party officials say women will be lucky to keep the 22 seats they now hold in the House. This year, 64 women won party nominations for the House, just eight more than in 1976. And, at this point, only two non-incumbents, state Sen. Jan Myers, a Kansas Republican, and state Sen. Frances Farley, a Utah Democrat, are favored. Both are running for open seats.

A handful of others have a shot at victory. Among the Democrats:

Dudley Dudley, leader of the 1980 draft-Kennedy movement, running for an open seat in New Hampshire (her motto is, "You can't forget the name, you won't forget the candidate").

Oregon state Sen. Ruth McFarland, who is suffering money problems in an uphill match against Rep. Denny Smith (R-Ore.).

Jane Wells Schooley, who has built up what party leaders call "the best grass-roots organization" in the country in her blue-collar district around Bethlehem and Allentown, Pa.

Among the Republicans:

Republicans Elise du Pont, wife of outgoing Delaware Gov. Pierre S. du Pont IV, who is trying to unseat Rep. Thomas R. Carper (D-Del.).

Judy Petty, a conservative who ran President Reagan's 1980 campaign in Arkansas, who is running for an open seat in the Little Rock area against Tommy Robinson, a colorful local attorney.

Jill Emery, who is seeking to unseat Rep. Stan Lundine (D-N.Y.) in western New York state.

A look at two of the races, those of Republican Francke and Democrat Schooley, tells a great deal about the state of gender politics in 1984.

The two articulate, young women are alike in several ways. Both are making their first attempt for public office. Both have raised unusually large campaign war chests. Both have been endorsed by major feminist organizations. And both trail incumbent male opponents.

But each faces unique problems.

Schooley, 35, is a product of the women's movement, a former vice president of the National Organization for Women who is proud of her work on behalf of feminist causes.

But this fall her feminist activities -- especially her support of legalized abortion and gay rights -- have become a liability in her hard-pressed blue-collar district. A vicious letter-to-the-editor and whisper campaign has risen up.

Her opponent, Rep. Don Ritter (R-Pa.), denies any connection with such activities. But the harshest public attack to date on Schooley was made by one of Ritter's top supporters at the opening of his campaign headquarters. Bernard V. O'Hare, chairman of "Democrats for Don," called Schooley's views on abortion and gay rights an "act of trespass" against the moral convictions of the Lehigh Valley.

Schooley's athletic-looking husband, Stuart, has taken to campaigning with her every night to counter rumors. But the candidate is deeply frustrated.

"Fear, ignorance and intolerance are always hard to fight," she said in an interview.

Francke faces an entirely different set of problems.

She is a moderate Republican running against a conservative Democrat -- four-term incumbent Rep. Harold L. Volkmer -- whose views on social issues are closer to President Reagan's than hers in a Democratic district where Reagan is exceptionally popular.

To upset Volkmer, Francke needs to ride Reagan's coattails and to pick up widespread support from Democrats and independents, especially in the university city of Columbia, where she resides.

This is a tricky business.

She is on shaky ground with conservative Republicans because she disagrees with Reagan and the Republican Party platform on legalized abortion, the Equal Rights Amendment and prayer in public schools.

She is on equally shaky ground with some feminist and women's groups that have endorsed her. "Some of them are so anti-Reagan they won't have anything to do with any Republican," Francke said.

So how does she campaign? She tells Republican groups, like one that met here last week, that "a vote for Ronald Reagan and my opponent is a canceled vote."

More dramatically, she has tried to make Volkmer the issue in the race. She calls him a "loner, not a leader," and is running a hard-hitting television commercial which shows bills sponsored by Volkmer being thrown in the trash as a voice notes that "Washington Monthly just named Harold Volkmer one of the 15 worst congressmen."

Schooley is taking a similar tack.

She accuses incumbent Ritter of being "out of step with the Lehigh Valley" for supporting Reagan budget cuts and social programs and opposing public service jobs.

"Since Don Ritter has been in Congress three steel mills have closed, 10,000 jobs lost, 41 textile mills have shut down," one of her radio ads says. "Ritter has voted not once but three times against targeting jobs in the Lehigh Valley."

This kind of message sells well in the steel mills, textile plants and senior citizens centers where Schooley campaigns. It also worries Ritter, although he says he is well ahead.

But Schooley complains that Ritter has tried to detour voters' "minds away from this area's economic crisis" by mounting a smear campaign against her.

"At every opportunity, he's creating a battle of the sexes," she said. "His whole attack is that he's running against a woman."

Ritter says Schooley has created a "battle of the sexes." He notes that she is the second female opponent that he has faced since 1978. "The major difference between this opponent and the others is not that she's a woman, it's that her stands on issues are so much more liberal than the mainstream of her party."