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WILLIAMSBURG, Va. — House Republicans have their Tea Party Caucus. They have their G.O.P. Doctors Caucus. And, joining the list of varied special interest caucuses, they recently picked up another influential but much more unofficial group — the Vote No/Hope Yes Caucus.

These are the small but significant number of Republican representatives who, on the recent legislation to head off the broad tax increases and spending cuts mandated by the so-called fiscal cliff, voted no while privately hoping — and at times even lobbying — in favor of the bill's passage, given the potential harmful economic consequences otherwise.

Representative Tom Cole of Oklahoma, part of the Republican whip team responsible for marshaling support for legislation, said the current makeup of House Republicans could be divided roughly into a third who voted in favor of the bill because they wanted it to pass, a third who voted against the bill because they wanted it to fail, and a third who voted against the bill but had their fingers crossed that it would pass and avert a fiscal and political calamity.

One lawmaker, Mr. Cole said, told him that while he did not want to vote in favor of the bill, he also did not want to amend it and send it back to the Senate where it might die and leave House Republicans blamed for tax increases. "So I said, 'What you're really telling me is that you want it to pass, but you don't want to vote for it,'" recalled Mr. Cole, who voted yes.

As House Republicans gather here in Williamsburg on Thursday for their annual retreat, the Vote No/Hope Yes Caucus is likely to come in for serious attention as party leaders and members of the rank and file try to map out an approach to coming confrontations with President Obama and Congressional Democrats that are certain to leave Republicans with uneasy choices.

The Vote No/Hope Yes group is perhaps the purest embodiment of the uneasy relationship between politics and pragmatism in the nation's capital and a group whose very existence must be understood and dealt with as the Republican Party grapples with its future in the wake of the bruising 2012 elections.

Ron Bonjean, a Republican strategist and once the top spokesman for the former House speaker J. Dennis Hastert, a Republican, described the phenomenon thusly: "These are people who are political realists, they're political pragmatists who want to see progress made in Washington, but are politically constrained from making compromises because they will be challenged in the primary."

The New Year's Day tax vote was a case study in gaming out a position on a difficult bill that many Republicans knew had to pass but was also one they preferred not to have their fingerprints on.

The Republican leadership itself seemed to reflect the ambivalence of their membership; Speaker John A. Boehner voted in favor of the legislation, while Representative Eric Cantor of Virginia, the majority leader, voted no. Even Representative Kevin McCarthy of California, the No. 3 Republican charged with securing votes for bills, voted against the deal. (Ultimately, 85 Republicans joined with 172 Democrats to pass it.)

"I think it's important that leadership provide an example, so either you're for it and you want your members to vote for it, and when you have confusion at the top, that leads to confusion in the rest of the ranks," said John Feehery, a Republican lobbyist and also a former top spokesman for Mr. Hastert. "They have to be much more coordinated, and they have to do a much better job explaining to the rank and file what's going on here."

Explaining his own vote to his local newspaper at the time, Representative Paul D. Ryan of Wisconsin, the Budget Committee chairman and a former vice-presidential candidate, seemed to acknowledge that some members of his party were not voting for a bill that they privately wanted to to pass, saying, "If you think a bill should pass, you ought to vote for it."

The phenomena occurred again this week as the vast majority of House Republicans, many citing spending concerns, abandoned a measure to provide relief for states hit by Hurricane Sandy, even though Republicans clearly wanted the measure to ultimately pass.

At the two-day retreat, aides said, Republican leaders are expected to emphasize that a united conference going forward will offer House Republicans the strongest negotiating stance on crucial coming issues like the debt ceiling limit and spending cuts. Conservative rank-and-file members, meanwhile, plan to express their frustration at feeling largely cut out of the deal-making process, and to request more chances to offer input.

"I think there will be a lot of looking back on the fiscal cliff vote," Mr. Cole said. "I think there will be some discussion on the divided leadership, saying, 'You guys need to sort this out, you need to be willing to make a decision and lead.'"

Still, he added: "I can make a pretty good case that our problem is less one of leadership than of followership. I'd be happy to just have some people who would follow decently."

Part of the problem House Republicans are struggling with is philosophical: What does it mean to hold the majority in the House, but still be the minority in a town currently under Democratic control? What is ideal, what is achievable, and where does that fine line of compromise lie?

And what are the limits of their own conference?

"Look, the reality is we control one-half of one-third of the federal government in a Democratic-run town," said Michael Steel, a spokesman for Mr. Boehner.

Of course, legislators reluctant to take potentially unpopular votes are nothing new. A classic example occurs with Congressional pay raises, where, said David Dreier, a newly retired California Republican, the adage is, "Vote no and take the dough."

In late December, Republicans encountered a similar challenge when Mr. Boehner put forth his "Plan B," an alternative measure to avert the tax increases and spending cuts that ultimately failed because of lack of support in his own party. Republican aides and representatives said that while the House Republicans privately had nearly 230 members in favor of the plan, they were not able to muster commitments for the actual 218 votes necessary for a majority.

On both Plan B and the fiscal legislation, Republicans said that many of the representatives ultimately recognized that the compromises were probably as good a deal as they could expect, and ones that were necessary to avoid a financial meltdown. Yet opposing the bills proved a politically safer and more ideologically pure move.

"Some members are worried about being primaried from the right, and some members don't want to be hounded by their constituents," Mr. Feehery said. "It's always easier to vote no. No one will yell at you if you vote no. They'll only yell at you in the grocery store if you vote yes."