A heavy fog blanketed this city Friday morning, turning the lots of unsold bulldozers into a yellow haze as 13,000 striking Caterpillar workers began a daylong procession, driving north to collect their last company paycheck.

The men driving the pickups, Fords, Chevys and Hondas are middle-aged because the once prosperous Caterpillar Tractor Co. had already laid off 8,000 people and the only workers left holding union jobs have a minimum of nine to 10 years' seniority.

On the Illinois River, the grain barges barely moved, backed up because of a bumper crop that forces farmers to sell at $2 a bushel corn that costs $3 to grow.

In good times and bad, Peoria has been a pocket of prosperity in the heartland of America, an island of productivity and well-being due to Caterpillar, a Pabst brewery, a Hiram Walker distillery and rich farmland.

For 26 years, Peoria has sent Republican Rep. Robert H. Michel to Congress, where he has climbed the ladder to House minority leader. During the 97th Congress, he engineered the conservative Southern Democrat-Republican coalition that enacted President Reagan's economic program.

In the past two years, however, Peoria has joined the rest of the smokestack cities of the Frost Belt in becoming a pocket of depression. Unemployment is 10.1 percent nationally, but in Peoria and neighboring counties it is 15 percent.

The economic nosedive has produced the most serious challenge to Michel in years.

G. Douglas Stephens, a 31-year-old lawyer with strong ties to organized labor but no past elective office, is conducting an energetic but underfinanced drive to unseat Michel. The polls show Stephens 13 points behind.

The Republican Party and its business allies are pulling out the stops to prevent what would be the most embarrassing defeat for the Reagan administration this year.

One of Michel's major assets is the belief among national Democratic leaders and those who control the flow of money from major unions that this contest cannot be won, that the recession has not yet converted central Illinois from the GOP to the Democrats and that Stephens will try hard and lose.

This assessment is supported by poll data, although statistics should make this prime territory for a Democratic challenge to Reaganomics.

Not only has Caterpillar laid off 8,000 workers and reduced its work force by 4,000 more through attrition, but when the United Automobile Workers contract expired it was the company's negotiators who walked away from the table and precipitated the union's strike.

If there had to be a strike, it could not have come at a better time for the company, according to financial analysts, and the UAW charged that it is "a company-engineered strike." The tractor company denies the charge.

The strike, in turn prompted Caterpillar to lay off 1,500 nonunion employes, and the shutdown is spreading to other manufacturers.

Earlier this year, Pabst closed its brewery, putting 750 people out of work, and Hiram Walker completed a three-year phased closure of the distillery, which eliminated 1,150 jobs.

"Two years ago," says Jim O'Connor, president of striking UAW local 974, "Reagan got eight out of 10" of the workers' votes in his union. "For 21 1/2 years, we had full employment. We had it good. We have members with $80,000 homes. They were going around wearing Reagan buttons."

With the layoffs and now the strike, O'Connor argues, as he points to his membership, "you are looking at a sleeping giant, and I think it's been awakened."

"Reagan and Michel and everything they have done has convinced my membership that their roots don't lie with the Republican Party," O'Connor says.

This is, however, an area where Republican Party roots extend back before the Civil War, where Democrats and organized labor are seen, in some quarters, as part of a distasteful, Chicago machine style of politics.

A Kiwanis and Lions Club conservatism, not the New Right, dominates; the voting patterns are hard to break, even when the worst economic conditions in more than 40 years coincide with a Republican administration.

Michel, returning here for the final four weeks of the campaign, complained that his as well as the administration's fight against inflation "has really been done the hard way, and the hard way is not having a doggone thing to promise the people."

Michel is by no means unarmed. According to his staff, he has raised $350,000, and is likely to reach $500,000 by Nov. 2. In addition, 40 GOP House colleagues plan to divert $100,000 from their campaign treasuries into his.

While Stephens has yet to buy any television time, Michel commercials dominate the airwaves. Later this month, Reagan will come to town with Charlton Heston and Pat Boone for an event the campaign describes as "Bob Michel and America."

For Stephens, this is a race that requires the strategy Republican House challengers used in 1980 to defeat senior Democrats. An exceptionally well-financed GOP used every means available, particularly television, to tie incumbents to the hard times.

Unfortunately for Stephens, he does not have the money for that kind of race. Aides complain that a promise from the Democratic National Committee to give more than $23,000 has resulted so far in only $2,000, and most of the unions backing Stephens have come across with relatively small contributions of $250 and $500, far less than the $5,000 maximum.

Stephens has raised about $105,000, and strategists optimistically hope to spend $35,000 to $40,000 on television in the closing weeks. Michel, in contrast, has already booked $35,000 worth of ads on just one of the seven television stations serving the market, and his aides believe he will end up buying the maximum the stations will sell.

While Stephens has been getting unusually intense coverage in the local media, his inability to buy television time early has made it difficult to try to capitalize on the heavy baggage Michel carries into the contest.

Not only was Michel the Reagan lieutenant for a tax and budget program that has failed to produce economic recovery, but, possibly more serious for the folks at home, he initially gave tacit approval to Reagan's decision to bar U.S. companies from providing material for the Soviet gas pipeline.

The marketplace is the marketplace, and a job is a job. The Reagan decision cost Caterpillar a $90 million contract.

Worse, it contributed to a shift in the Soviet Union's marketplace decisions. Two years ago, Caterpillar had 85 percent of the Soviet market for tractors, bulldozers and other earth-moving equipment, while its major international competitor, Komatsu in Japan, had 15 percent. Now, Komatsu has reversed the ratio.

Both company and union officials say that the sanctions "turned us into an unreliable market for the Russians."

Michel's initial position, that the president "should be given the benefit of the doubt," has turned into a political disaster. He has had to make a complete reversal that included sponsorship of a failed effort in the House to overturn the sanctions.

On the Caterpillar picket lines, where the anger at the GOP is almost tangible, and in the farmland south of here, there is doubt about Michel and the Republican Party, although it is not clear that this would translate into serious defections Nov. 2.

"I don't know," said Robert Dutton, who owns and operates a 1,200-acre farm near Manito and voted for Michel in the past. "I listened to Stephens' ads, and they make you wonder whether Michel's so honest and righteous."

Bob Larsen, who manages the Green Valley Farmer's Grain and Coal Co. and talks daily to farmers storing their grain, says he remains a loyal Michel supporter, but warns that "the last time, a lot of the farmers voted Republican, but this time they won't"

Still, polls suggest that Michel's intense media campaign and Stephens' lack of one have taken the edge off the latter's challenge. One early poll showed Stephens within 8 or 9 percentage points, but after Michel began his commercials, he dropped to about 16 points behind.

Since then, according to Michael Johnson, a Michel aide, Michel's lead has narrowed to 13 points.

Both are gaining among undecided voters, but Stephens is getting more -- and "that's not comfortable," Johnson said.

He asserted, however, that Michel now has so much of the committed vote that it would take an exceptional development for Stephens to turn the contest around.