One night shortly after Thanksgiving, a few dozen young Republican conservatives gathered at the home of Heritage Foundation executive Betsy Hart to hear former presidential aide Lyn Nofziger offer a briefing on how best to challenge a sitting president.

Nofziger, who helped mount Ronald Reagan's unsuccessful primary run against incumbent President Gerald R. Ford in 1976, gave them an answer they apparently did not want to hear. Ford, they were told, was considered a weak target but had still proved formidable. President Bush, for all of his recently acquired political liabilities, remains far from weak, Nofziger said.

The disgruntled conservatives who listened to Nofziger that night, however, are not likely to be easily discouraged. Nurturing a fire that was ignited by the president's reversal last May of his no-new-taxes campaign pledge, conservative subsets within the GOP have begun actively and angrily debating the future of their cause under Bush's leadership.

Words like "betrayal" and "discontent" are increasingly being used in these discussions. Bush, who was always viewed with a measure of suspicion among the most conservative members of his party, confirmed worst-case scenarios for many when he retreated on the tax issue. Since then, many have been unhappy with his foreign policy stands on the Soviet Union and the Middle East. Bush, they argue, has not yet persuaded them that other nations are sharing enough of the military burden in the Persian Gulf or that Kuwaiti independence is a just enough cause for which to risk American lives.

Another segment of the discontent is rooted in the administration's well-publicized recent disarray on domestic issues ranging from affirmative action to the leadership of the Republican National Committee.

The GOP dissident faction has no single leader, but most of its members share a common complaint: They fear Bush has replaced the Reagan agenda with a more moderate and, in their view, dangerously conciliatory path.

Former Delaware governor Pierre S. "Pete" du Pont IV, who ran against Bush for the Republican presidential nomination in 1988 and founded a group this week called the Committee for Republican Leadership, said his aim is to "glue that whole Reagan coalition back together again."

A seven-page statement du Pont composed about the new group laments that "the clarity of our principles has been dimmed in recent months" and calls for a campaign against tax increases.

Included in du Pont's new organization are a number of Republicans -- including Sen. Trent Lott (R-Miss.) and Reps. Vin Weber (R-Minn.) and Newt Gingrich (R-Ga.) -- who long have been unhappy with the direction of their party's administration. Former Reagan speechwriter Peggy Noonan and Texas Republican National Committee member Ernest Angelo Jr., are also listed alongside former Reagan domestic policy adviser Gary Bauer and evangelist and former presidential candidate Pat Robertson.

Du Pont, who said in an interview there are "no conceivable circumstances" under which he would challenge Bush in 1992, is typical among the unhappy conservatives in that he lays much of the blame for what he sees as the downfall of the GOP at the door of White House budget director Richard G. Darman, whom he calls the "architect of abandonment."

"You can't simply reverse the central premise of the party's existence for no real reason and not have your loyal foot soldiers say, 'What's going on?' " du Pont said of the tax reversal.

Congressional critics -- led by Gingrich, Weber and Lott -- have been making the rounds deriding Bush by deed, if not by name. In a November speech to a meeting of conservative state legislators, Gingrich criticized the current Republican administration as harshly as he did the Democrats, likening administration officials to "Kennedy school technocrats," epitomized by Harvard-educated 1988 Democratic presidential nominee Michael S. Dukakis.

"Politics is a reflection of what you dream, what you value, what you hope," he said. "And it involves tremendous conflict."

The conflict, Republican officials concede, has already begun to erode a significant portion of the president's political base. Yet another discontented segment of the GOP base can be found among those who listened to Nofziger at Betsy Hart's house.

Those young Republicans are considering fielding a slate of single-state, favorite-son candidates in 1992. The goal, Hart said, would be to embarrass the likely nominee in key states such as New Hampshire.

Gordon J. Humphrey (R), who retired from the U.S. Senate to become a New Hampshire state senator, has been approached about undertaking such a challenge in his state, where a fair number of former Bush supporters are displeased both with the president and his chief of staff, former New Hampshire governor John H. Sununu.

"There is absolutely a mounting belief that Bush needs to be challenged in '92," said Hart, who is director of lectures and seminars at Heritage, a conservative think tank. "The issue is, Bush calls himself a conservative but is not."

Asked whether the conservative backlash might be undermining the GOP during a key period, Hart responded: "George Bush is destroying himself and his presidency quite nicely without any help from us."

Republican National Committee spokesman Charles Black, who ran Housing and Urban Development Secretary Jack Kemp's campaign for the Republican presidential nomination in 1988 but has served as the White House's key political adviser since RNC Chairman Lee Atwater became ill earlier this year, dismisses much of the disgruntlement as typical midterm policy debate.

He said the president supports most of the items the conservatives back. "Some you can't do right now. He may differ on timing and tactics, but there are no ideological cleavages. If you put the whole thing in context, around the country, rank-and-file voters and party activists are very happy with George Bush," Black said.

Another close Bush adviser agreed: "When you're in a tough period -- as the president has been lately -- it makes it easier for them to go out and generate a lot of noise."

Bush appeared to have found a way to satisfy some of the conservatives when he selected former education secretary and drug czar William J. Bennett to succeed Atwater as party chairman. But Bennett's decision to reject the RNC job immediately reopened the barely healed wounds.

The most unhappy members of the conservative movement are already floating lists of possible 1992 challengers that include du Pont, Bennett, Robertson, retiring Sen. William L. Armstrong (R-Colo.) and columnist and former Reagan aide Patrick J. Buchanan. None of these men, Nofziger said, now has a base that can begin to rival the one Bush built during two national campaigns and a vice presidency.

"I've been through this," said Nofziger. "A sitting president controls the establishment, the state committees, the national committee. Republicans who are professional activists turn to the president for leadership. Very few would screw up the courage to go out and challenge George Bush in a primary.

"I just think anybody who thinks they're going to run . . . against George Bush and beat him -- they're out of their minds," Nofziger said.