CHICAGO -- Rep. Lynn Martin (R-Ill.) has been on a fund-raising treadmill.

Her challenge to Sen. Paul Simon (D-Ill.) is the best-financed in the nation, thanks in large part to impressive support from the Bush administration. President Bush has come to Illinois twice to raise money for her campaign. Barbara Bush and most of the Bush Cabinet have also campaigned for her here.

But the $4.7 million Martin raised through Oct. 17 is not enough. She is far short of her $8 million fund-raising goal and had little more that $250,000 left in the bank. As a result, she did not have enough money to buy time on television for a full, critical month, a drought that ended only last week.

In contrast, Simon raised $7.8 million through Oct. 17. His television commercials have aired steadily since before Labor Day, and he still had more than $1 million available to spend.

The four-week gap in Martin's television advertising illustrates how she has had to run hard to try to stay in place. She needs to raise money to buy television time to try to increase her standing in the polls so she can raise more money to buy more television time.

Virtually unknown outside her House district in the northwest corner of the state when the campaign began, Martin had to spend more than $650,000 of her media budget in a two-week, statewide advertising barrage last spring to increase her name recognition from 18 percent to about 50 percent. Now Martin's campaign aides say her name recognition is probably more than 80 percent, but the polls still show her far behind Simon a week from Election Day, and she is still having trouble raising the money needed for more paid television.

The challenger's contributions have not dried up, spokeswoman Kathy Lydon said. But the inability to buy time on television hurts fund-raising. "Being on the air generates interest in the campaign, which generates contributions," she said.

Thus, in an era when half a campaign budget generally is allocated for television, the challenger is finding out just how difficult it is to start a race with little statewide name recognition and then raise the money needed to run effectively against an incumbent who has a national fund-raising base.

As the campaign winds down, both candidates say they are weary of the relentless chase for campaign money. They dial strangers to plead for donations, sign emotional direct-mail appeals for cash, and glad-hand at fund-raising picnics on the Illinois prairie and $1,000 dinners in Washington and Beverly Hills.

"If it wasn't for television, we'd have been finished raising money in March," an exasperated Martin said in an interview the day before Bush flew into Chicago late last month for his second fund-raising appearance.

Simon agreed that raising money "takes far too much time. It distorts the process. . . . We are excessively responsive to the financially articulate."

Martin's fund-raising problems are compounded by the fact that Illinois is a large state with 11 separate media markets, including the nation's third-largest television market, Chicago. Raising the money to make a good week's "buy" in Chicago and six other Illinois cities costs more than $280,000. Adding fringe markets in other states can boost the price tag to more than $325,000 a week -- more than the total Martin spent in her last House race.

Martin's campaign also is vying for attention for donations and free media with a heated governor's race and other city and statewide contests. The GOP candidate for governor, Jim Edgar, has raised $10.8 million -- $6 million more than Martin. Edgar's democratic opponent, Neil F. Hartigan, has raised $7.6 million, slightly less than Simon. Unlike the federal system, there are no limits to what individuals, corporations or unions can give in Illinois state races.

When Martin started her race against Simon, she said, "I don't think I truly understood" the importance of fund-raising. "The money, because of television, is incredible."

Voters, Martin added, "have to look at this, and they're not dopes. They say, 'Wait a minute. Who gets served first in this cafeteria?' And I can tell them I don't even remember who contributes to me. But do they believe me?"

The challenger announced recently that she will set her own limits on campaign money -- taking no more than 25 percent of the total from donors outside Illinois or from political action committees (PACs). Martin has criticized Simon for raising more than half his larger donations from outside the state.

Simon said he, too, is concerned about how fund-raising affects candidates and the public. If he agrees to support an amendment favored by an individual who raised $25,000 for him, Simon said, "in the back of my mind I wonder if he thinks I'm agreeing with him because of his money. In the back of his mind, he may very well be thinking, 'Maybe that's tipping the scales in my direction.' So it corrodes the system. It puts a factor in there that's not desirable.

"And in the public mind, with all the money, people are just bought and sold," Simon said. "It's frankly more sophisticated than that. But it is not a good system."

Of course, to run their race, Simon and Martin have swallowed their misgivings and energetically joined in the money chase.

When she decided to challenge Simon, Martin was not without assets. They included her friendship with Bush, and with Illinois and national business leaders.

In early 1989, Simon also looked like a vulnerable opponent. He was coming off a failed presidential campaign and was so busy paying off that debt that he had only $38,000 in his Senate campaign fund. But he had assets as well: a 40,000-name donor list and the support of organized labor and pro-Israel PACs.

Simon spent $5.3 million in narrowly defeating Sen. Charles H. Percy (R-Ill.) in 1984, $1.8 million of it on advertising. He and his strategists set an $8 million budget for the 1990 campaign after learning that the same size media buy would cost $4.1 million now.

The incumbent then hired three fund-raising consultants to help find the money. Amy Zisook, a veteran from Simon's first Senate race, covered Illinois. Another firm did national fund-raising, and a third did Washington events.

They have been so successful they can complain only that the governor's race has competed for donations. In addition, the senator's big lead in the polls is making it harder to convince loyalists in the final weeks that Simon still needs their money, they say.

Simon's largest single source of money has been about $2 million from direct-mail solicitations. In one mailing sent to many Jewish Americans after Iraq invaded Kuwait in August, he invoked the name of Iraqi dictator Saddam Hussein as a peril to Israel. Martin, he said, opposed U.S. aid to Israel on nine of 11 key votes. He recalled that he won his race against Percy "for one reason: the generous help of individuals like you."

A Simon strategist said such appeals to the pro-Israel community have not been as productive in this campaign as they were in 1984 because "there isn't a Chuck Percy enemy." In 1984, Percy was chairman of the Senate Foreign Relations Committee, and his support for arms sales to Arab countries was a key selling point to pro-Israel contributors to Simon.

The Simon camp is proud that its list of donors has grown to 70,000. But using the mail and the telephone for small donations has pushed their fund-raising costs up to about $2 million.

Larger events that bring in PAC dollars or $500 and $1,000 donors are more cost effective. The campaign's first large event, in June 1989 at a Chicago hotel, raised more than $500,000, still the largest of the campaign. The next most successful was last week when an appearance by entertainer Harry Belafonte raised about $350,000.

In between, Simon's money team has sponsored scores of smaller fund-raisers. They included an Oct. 2 Washington reception that listed a 62-member host committee of lobbyists and raised $70,000, and trips to Boston, New York and California -- where the Valet Girls of Malibu were paid $409 for parking cars for one event. The money team also raised funds at a Chicago Cubs baseball game and -- playing off a Martin gaffe early in the campaign -- at a "redneck" party in Simon's downstate home area near Carbondale.

"We make them {events} as gimmicky as we can so they'll be something interesting people will want to go to," Zisook explained. "But once you get over a $50 ticket price, gimmicks don't work. That's a real financial investment for many people."

Simon also has raised more than $1.3 million from PACS -- 17 percent of his total -- the most generous being pro-Israel and labor groups. He has about 500 donors who have given the $1,000 maximum personal contribution allowed under federal law, according to an aide.

Martin's largest source of funds has been $1.5 million from events featuring Bush administration figures. A presidential appearance last November generated $700,000; another late last month added $500,000. A Barbara Bush trip raised $250,000, and a Washington event sponsored by Cabinet wives Georgette Mosbacher and Honey Skinner collected another $100,000.

Campaign manager Mark Schroeder noted that "practically every member of the Bush Cabinet" has traveled to Illinois -- at the challenger's expense -- to help Martin. Those appearances often attract local television news coverage, a priority for a challenger "that generates interest in the race," he said.

Through September, the Martin campaign had 18,653 donors, according to Lydon. With the aid of finance chairman Richard Morrow, chairman of Amoco, and Robert Stuart, retired head of Quaker Oats, she has attracted about 715 donors who gave the maximum $1,000.

Martin's team has also arranged scores of lower-priced events. One featured a 10-minute video on the candidate shown in 150 homes around the state on the same day in August. Another was a picnic on a farm near Moline that attracted 500 people who paid $10 each.

She also has benefited by infusions of cash from several national GOP fund-raising committees, and her campaign has raised more than $1.1 million from PACs -- nearly a quarter of her total.

Martin admits her middle-of-the-road politics do not attract ideological donors. "There's no madly moderate big interest group," she said. "There's no cadre for common sense. That's part of the flaw" in the system.

In the meantime, the challenger continues on the treadmill. She had a fund-raising breakfast Saturday in the Chicago suburb of Northbrook that was expected to raise another $5,000 or so. That's about half the cost of one 30-second television ad on a top-rated show on just one Chicago station.