President Bush and the Republican Party face a tough task of coalition-building in the wake of a midterm election that weakened the GOP's Sun Belt base, revitalized its long-downtrodden moderate wing and left some conservatives talking mutiny.

Hopes that 1992 would bring relief from the Republicans' permanent minority status on Capitol Hill were badly dented when the off-year voting produced traditional losses for the president's party instead of hoped-for gains.

At the White House, Bush kept out of sight all day and offered no public assessment of the election in which he had campaigned so vigorously. Officials said he telephoned 50 GOP candidates nationwide, offering congratulations or condolences, while advisers began wrestling with a future that one called "a lot more complicated than Ronald Reagan's was in 1982."

House Minority Whip Newt Gingrich (R-Ga.), who has embodied GOP hopes of achieving majority-party status in 1992 and who barely survived his own reelection race, called it "a very sobering experience for all of us who thought we had lots of momentum heading into the 1990s." Gingrich said Republicans will now be forced to "reassess where we are going."

Republican losses -- one Senate seat, nine House seats and one or two governors (depending on the still-undecided Arizona race) -- were far from severe by historical standards. But during the past 12 months, when Bush was at stratospheric heights of popularity and the economy was steaming along, Republicans had allowed themselves to think they might break the pattern of midterm losses. Instead, they lost key races in the growth sections of the country, slipped nearly beyond the point of return in the battles for Senate and House majorities next election, and gave up some leverage over the way legislative and congressional districts will be drawn next year for the 1990s.

"All we have to do is end the civil war among Republicans, begin reassembling the national coalition we had the past decade and lost the last year, and find a compelling message to differentiate us from Democrats so they don't define us," one Republican official said.

Several Bush allies suggested those tasks would require substantial strengthening of the White House political operation, now controlled by Chief of Staff John H. Sununu. But at a brief appearance at a senior staff meeting, where he gave a pep talk to his aides, Bush dropped no hints of coming changes, and some present viewed the appearance as a signal of support for Sununu.

The continuing illness of Republican National Chairman Lee Atwater, who is under treatment for a brain tumor, has left a gap in the partisan advice Bush receives. GOP sources say that function is likely to be filled by the time the RNC meets early next year.

Officially, the White House took the stance that nothing that happened Tuesday required repairs. Presidential spokesman Marlin Fitzwater said, "When the final record of the 1990 elections is written, we believe that the Republican Party will be strong and its leadership secure. The president will face essentially the kind of opposition Congress that he faced in the first two years, and the veto will be a large part of our legislative strategy."

But those words offered cold comfort to Capitol Hill Republicans who had dreamed of being part of what Gingrich called "a governing conservative majority." With Tuesday's losses, Republicans would need a 51-seat pickup to end the Democrats' 38-year dominance of the House. The biggest GOP gain of the postwar period was 56 seats in 1946.

"The prospects of significant Republican power in Congress are very remote," said Rep. Robert G. Torricelli (D-N.J.). "The possibility of Republicans either gaining control of the House or effective control through a conservative coalition is lost for many years."

In the Senate, the task is less implausible, but still difficult. With 44 seats in the incoming Congress, Republicans would have to make a net gain of six seats for the vice president to break a tie in their favor. Democrats defend 20 seats to the Republicans' 14 in 1992.

Steve Hoffman, a veteran Republican congressional staffer, now a private consultant, said those recruiting Senate candidates for the next election "will find it very much harder to enlist good people," because the four House members recruited as Senate challengers this year in Hawaii, Illinois, Iowa and Rhode Island "all had their clocks cleaned."

Hoffman also suggested that with their reduced numbers, House Republicans "will become even less relevant to White House strategy."

While congressional Republicans contemplated a bleaker future, some restive conservative intellectuals and political operatives began talking about creating a power center that could challenge the White House for the allegiance of restless GOP officeholders and voters. Some of their hopes centered on William J. Bennett, who let out word on Election Day that he is leaving his job as coordinator of the war on drugs.

Burton Yale Pines, an official of the Heritage Foundation, where Bennett is reportedly headed, circulated a paper among other conservatives suggesting "open opposition" that "would show the public that conservatives are not responsible for . . . the economic and other disasters toward which Bush and his advisers are driving the nation."

Conservatives have become increasingly critical of the administration since the bonds of anticommunism were dissolved by improving U.S.-Soviet relations. When Bush abandoned the no-new-taxes pledge of his 1988 campaign in order to negotiate a budget-deficit agreement with congressional Democrats this fall, the conservatives moved into open rebellion.

"If Bill Bennett begins to articulate what's wrong with George Bush's Washington," Pines said in an interview, "people will rally around him."

Bennett, still a member of the administration, would comment only that "there needs to be a good discussion between the White House and the congressional Republicans about what the party's about." Friends said they doubted he would risk his own presidential ambitions on a "kamikaze mission" against Bush's renomination.

But Eddie Mahe, a veteran GOP operative, predicted in a separate interview that "Bush will be opposed for renomination and the challenge will be serious enough that he won't be able to ignore it." Mahe also predicted "there will be a big battle over right-to-life" language in the 1992 Republican platform.

He and others commented on the striking phenomenon of Republicans losing governorships on Tuesday in the key Sun Belt states of Florida and Texas while simultaneously adding Massachusetts, Vermont, Ohio, Michigan and Minnesota to the governrships they retained in Illinois, Iowa, Wisconsin, New Hampshire and Maine.

Several of the newly elected governors -- notably California's Pete Wilson, Minnesota's Arne Carlson and Massachusetts's William F. Weld -- are from the moderate wing of the party and opposed restrictive antiabortion laws in their campaigns. The last three GOP platforms have taken a strong antiabortion position.

Paul Weyrich, president of the conservative Free Congress Foundation, commented that "it seems as if the Republicans are moving back to a pre-Reagan party, where the base is more to the left and the East and where the emphasis is less on appealing to conservative middle-class Democrats than in the past. I'm not sure where this is going to take us, but . . . I think Bush is more comfortable with that shift."

But many Republicans believe that without the appeal to the blue-collar workers, the evangelicals and the young people that Reagan attracted to the party, the GOP's grip on the White House is in danger and its chances of becoming a majority party nonexistent.

Edward J. Rollins, the manager of Reagan's 1984 campaign and now co-chairman of the National Republican Congressional Committee, said yesterday that "the coalitions today need some work. There's no question that blue-collar Democrats -- some of them -- went home. Some Republicans are not as pleased with Republican positions today as they may have been. The president has two years to get all that together."

White House anger at Rollins's memo to GOP congressional candidates that they could feel free to oppose Bush's budget-deficit agreement contributed to the sense of disarray that marked the midterm campaign and brought criticism to Sununu and others in the Bush entourage.

Yesterday, Secretary of Housing and Urban Development Jack Kemp, who publicly disagreed with the White House strategy, said that "the tax issue is a very important one, and if the Republican Party hopes to win in 1992, we have to -- I don't want to say back -- we have to go forward to the kind of . . . policy that allows people the greatest possible . . . return. We have to meet the Democrats' soak-the-rich theme head-on."

Many Republicans and Democrats pointed to evidence of tax resistance as a driving force in many, if not all, the midterm campaigns. "Republicans who voted against the {budget} package probably did better," Bennett said, "and that's significant." Much was made of the fact that Sen. Rudy Boschwitz (R-Minn.), the only Senate incumbent in either party to be defeated Tuesday, "ran two weeks of ads bragging about his bravery in supporting the budget deal and then brought in Bob Dole and Pete Domenici {the principal Republican architects of the tax-raising agreement} as his character witnesses," as one conservative put it.

But even as Republicans mourned the issue that got away, several of them -- and some Democrats -- suggested that Tuesday's voting had proved the potency of another issue -- affirmative action and quotas.

Used with bluntness by Sen. Jesse Helms (R-N.C.) in his successful reelection race and with more subtlety by Sen. Pete Wilson (R-Calif.) in winning the California governorship, the issue packed a power that left many Democrats stunned.

Mike Donilon, the pollster for Helms's defeated black challenger, Harvey Gantt, said: "Democrats need to understand that the campaign Helms ran against Gantt was not a campaign from the 1950s. He raised cultural and racial issues that are battlegrounds for the next 10 years."

Meantime, some Republicans found they could make significant headway into black constituencies. Jim Edgar, the winner of the Illinois gubernatorial race, and South Carolina Gov. Carroll A. Campbell Jr. (R), running for reelection against a black opponent, each received one-fifth of the black vote, according to exit polls.

Campbell, the leader of Bush's 1988 campaign in the South, cited the parallels in his and Edgar's race as evidence that the old coalition could be rebuilt. "Our philosophy," he said, "is that government provides an opportunity, not a guarantee. We know we can appeal broadly with that approach, without going too far to the left to do it."

"Obviously the South is volatile," he said, "and it's going to have to be contested. But in the Midwest, you see the old, traditional Republican base coming back again, and that is a new strength Bush can build on."

Staff writer Tom Kenworthy and political researcher Bruce Brown contributed to this report.