Bob Michel, the gentleman from Illinois, the "Mr. Nice Guy" of House Republicans, toiled for years in the nether reaches of the Appropriations Committee before emerging, in 1975, to the flickering limelight of minority whip.

"In 24 years as a minority member, you've got to scrap for everything," Michel said. "I've been present in the day-to-day fisticuffs. Now I feel I've earned the opportunity to move from the number two to the number one spot."

But a younger, flashier midwesterner, Guy Vander Jagt of Michigan, is challenging Michel's effort to succeed Minority Leader John Rhodes of Arizona, who is stepping down from the post voluntarily. Vander Jagt, the honey-voiced orator who keynoted the Republican National Convention in July, is an architect of the stunning GOP gain of 33 House seats, raising some $10 million a year as chairman of the National Republican Congressional Committee.

That extraordinary gain, combined with the election of about 30 conservative Democrats who tend to vote with Republicans, may well make the next minority leader as powerful as the speaker of the House.

Now that Republicans control the White House and Senate, the House is expected to be the pivotal battleground for Ronald Reagan's legislative agenda. The man elected to be minority leader will determine to a great extent how that battle is fought between conservatives and liberals, Republicans and Democrats, perhaps for the next decade or more.

The contest between Michel and Vander Jagt, both staunch conservatives yet as different in style as the tortoise and the hare, turned into a sharp, personal struggle as the vote, scheduled for today, approached and the race became too close to call. Rumors flew back and forth across the House that Michel was strong-arming colleagues with the threat of withholding committee assignments. Vander Jagt was calling in his chits with the 52 freshmen, who need no reminder as to who signed the $10,000 and $20,000 checks many received from the campaign committee.

"Any leadership race is as personal as you can get," Vander Jagt said. "It's eyeball to eyeball. Promises and rewards are nothing unusual. This is one of the cleanest, purest races in history."

Burly, balding and bespectacled, Michel, 57, is normally a man of great humor, with the all-American manner of his hometown of Peoria. But as the longtime pitcher on the congressional Republican baseball team, he's known for his hardballs. Now he's zinging them at Vander Jagt.

"We have different personalities," Michel said in an interview in his gold-carpeted, chandeliered chambers in the Capitol. "I've never been all that interested in personal aggrandizement as Guy has. I don't crave the spotlight. I get more joy and fun out of trying to orchestrate the talents of the others and trying to extract the best. I don't have this insatiable lust to be 'Mr. Speaker.' I just want to be Bob."

Michel's lieutenants, busy by the dozen collaring old friends on the floor, liken it to a match between "a showhorse and a workhorse." Michel echoes the theme. "It takes more than a TV image to get things enacted into law," he said. "You can make beautiful speeches, but the bottom line is going to be enactment of the Reagan program.

"Let's not forget we're still down 51 votes. Guy Vander Jagt has no experience on the floor and he'd be rebuffed on the other side of the aisle because he's been such a political partisan. A day-to-day diatribe would not serve the political process."

Vander Jagt, 49, son of a successful Dutch-born farmer, represents a conservative rural district on Lake Michigan's western shore. In the last six years he has traveled 500,000 miles, giving fiery speeches for obscure congressional candidates, and collecting in the process a stack of IOUs. He turned in his glasses for contact lenses, learned how to cultivate the press and, by the time he reached Detroit last July, was being mentioned as a vice presidential candidate.

"This leadership race doesn't matter a whit to the average guy in the coffeehouse," Vander Jagt said in a breakfast with reporters last week. "House Republicans are a forgotten minority of a forgotten body. If people pay attention, they focus on [Speaker Thomas P.] Tip O'Neill. That's why we need someone who can project to the American public . . . Inevitably one winds up on 'Face the Nation' or 'Meet the Press.' I think I would be a more forceful spokesman than Bob Michel."

Reagan turned to him for the keynote, Vander Jagt remarked, because he wanted "the best damn speaker in the Republican Party."

Vander Jagt contrasts his own successes with Michel's two-year tenure on the congressional campaign committee during the Watergate years when Republicans lost heavily. and, Vander Jagt added, "When Bob Michel was chairman, in the last 11 issues of the monthly magazine, he had big articles about himself 12 times."

The Michigander, who once tried to save souls as a minister before he went into politics, said he could easily compromise with Democrats "when conciliation will win votes. But when it won't we need aggressive confrontation that will really put their feet to the fire."

Other important leadership posts among House Republicans are also up for a vote this week, including the whip position contested by mild Missisipian Trent Lott and Bud Shuster (Pa.) who is praised for his record as head of the Republican Policy Committee. Jack Kemp (N.Y.) and John Rousselot (Calif.) are the favorites in the race for chairman of the House Republican Conference, which also includes Bill Goodling (Pa.) and Thomas W. Kindness (Ohio).

Richard B. Cheney (Wyo.), Marjorie Holt (Md.) and Eldon Rudd (Ariz.) are running for chairman of the Republican Policy Committee.

In the minority leader's race, Michel's image as a loyal, somewhat passive sidekick to Rhodes may hurt him. Rhodes has been criticized for lacking inspiration. However, Michel is deemed to be ahead among incumbent congressmen, who prefer a legislative technician.

"The American people are going to expect major changes," says Olympia Snowe, a second-term Maine Republican. "It's going to be incumbent on us to produce. I'm going to have to answer to my constituents." Snowe is supporting Michel, although she said she has received telegrams endorsing Vander Jagt from the Maine Osteopathic Association and the Maine Innkeepers Association.

Such outside pressure seems mainly to be coming from the Vander Jagt camp. He has the endorsement of the National Conservative Political Action Committee and the Society of Association Executives, a group of lobbyists.

Vander Jagt supporters include Rep. David Stockman, who says his Michigan colleague can "rally the troops," a key quality if Republicans are to achieve a majority in 1982. Freshman John LeBoutillier (N.Y.) sees it as a race between "old school and new school. Vander Jagt's a little less old-fashioned."

Barber Conable (N.Y.), ranking Republican on the Ways and Means Committee, prefers Michel, however, because "you need someone who will slug it out in a somewhat uninspired fashion, rather than someone who will summon thunderbolts of oratory."

But Conable isn't predicting the outcome of today's secret ballot. "One of the less attractive aspects of this craven collection is that both candidates have a majority of votes pledged to him," he said.