While no agreement on a deficit reduction compromise is yet in sight, House Republican leaders are working on a strategy to muster GOP votes for what would likely be a politically painful package for the conservative-dominated majority.

It may prove impossible for Speaker John A. Boehner of Ohio and his leadership team to find 218 votes in the Republican Conference for legislation that would almost certainly include tax increases. But although Boehner will have to rely on Democratic votes to help pass whatever deal he cuts with President Barack Obama to avoid automatic tax increases and spending cuts beginning Jan. 1, he will at least want to have the backing of a majority of Republicans.

Recognizing that they cannot afford to wait until the last minute to determine where the votes are in their conference, Republican leaders are discussing the outlines of potential deals with the rank and file. Alternative revenue- raising proposals were presented to the conference last week, including one plan that would cap deductions at $50,000. Republican leaders also talked about how much public support various revenue proposals have received in public opinion polls.

Some conservatives remain reluctant to fall in line. GOP Rep. Tim Huelskamp of Kansas, who says he opposes any tax increase, characterized one leadership presentation as, “OK, let’s pick which tax increases we’re going to cave on, when 238 of us said we would never do such a thing.”

Huelskamp was one of three conservative House Republicans who lost choice committee assignments this week as a result of action by the leadership-controlled Republican Steering Committee.

GOP leaders circulated talking points last week to buttress the Republican position that raising revenue through limiting tax breaks is preferable to raising tax rates. The document cited a Winston Group survey conducted earlier this month. “Sixty-five percent of those surveyed preferred a deal that wipes out ‘special interest tax loopholes and deductions commonly used by the wealthy’ over an approach that raises tax rates on ‘Americans earning more than $250,000’ on Jan. 1,” the GOP document said.

Republican lawmakers need little persuasion to support additional spending cuts. But Rep. Steve King of Iowa said an emphasis on spending cuts could help Republicans swallow tax hikes. “I think that’s something else that Republicans should be discussing,” he said. “This is what we get in exchange for revenue enhancements.”

Aides to Boehner and Obama continue to talk almost every day, according to people with knowledge of the negotiations.

Some House Republicans — as well as some of their Senate colleagues — have complained about the secrecy surrounding the high-level fiscal negotiations. “I’m bemused. This isn’t how you bring together a conference that is going into the 113th with fewer members in its majority,” said Rep. David Schweikert of Arizona, a restive conservative who was stripped of his seat on the House Budget Committee earlier this week. “For those of us on the conservative side, we care a lot about the details.”

Republicans in both chambers agree it is important that Boehner be able to win the support of most Republicans for any bargain he makes. If the Senate votes first on a fiscal compromise, a large bipartisan vote there could make Boehner’s task somewhat easier.

“The speaker can’t remain the speaker if he can’t continuously command a majority of the majority,” said Rep. Tom Cole of Oklahoma, a member of the House GOP whip team. “That’s just politics 101.”

Boehner has told Republicans he disagrees with Cole’s view that the GOP should accept the White House demand to extend all current tax rates except those for couples earning more than $250,000.

Sen. Roy Blunt of Missouri, vice chairman of the Senate Republican Conference and a former House GOP whip, said senators will be watching whether any debt deal meets the “majority of the majority” standard in the House. “It doesn’t have to maybe be a huge majority,” he said. “But unless the president wants to never get anything else done as long as he is the president and John Boehner is the speaker, they have to come up with an agreement that a majority of the speaker’s majority will vote for.”

GOP lawmakers are waiting for more details on the framework Boehner suggested in a Monday letter to Obama. They generally concede that the president has superior leverage in the current negotiations, and they worry that if a deal is not reached, the public will blame Republicans.

In a Washington Post-Pew Research Center poll released Tuesday, 53 percent of respondents said they would blame Republicans if the fiscal cliff deadline passes without action, while 27 percent said Obama would deserve more blame.

“I want an agreement that drives down the debt-to-GDP,” said Rep. Austin Scott, R-Ga., who reserved judgment on Boehner’s plan until he sees specifics and scoring by the Congressional Budget Office.

Rep. James Lankford, R-Okla., also withheld an endorsement of Boehner’s proposal to include $800 billion in new revenue over 10 years. “I’ve got to see all the details on that,” Lankford said. “I am supportive of the speaker and what he is trying to accomplish. That number is the same number he had last summer, so that’s not changed. That’s not something new.”

Senate Ponders Challenges

Senate Majority Whip Richard J. Durbin of Illinois said Democratic leaders in that chamber have not discussed the structure of floor votes on a possible debt deal. “The later it gets, the harder it gets,” Durbin said. “Until we have an agreement, nobody is seriously discussing the procedural challenges.”

Durbin said those challenges would include staffing during the holiday period, drafting and vetting the necessary legislation quickly, and the possibility of inclement weather that could hinder senators’ travel schedules. Durbin and other lawmakers recalled this week that the Senate passed its version of the health care law on the morning of Christmas Eve in 2009.

Senate Minority Whip Jon Kyl, R-Ariz., predicted that negotiations will be lengthy, but he said it remains possible to wrap things up by Dec. 21.

Other conservative GOP senators, including Mike Lee of Utah and Rand Paul of Kentucky, said they might use procedural tactics to slow down any fiscal compromise if they do not think senators have been given enough time to study the details. “I’m not going to vote for it just because they’re running a little late,” Lee said.

“Most of the deliberations seem to be going on behind closed doors. We’re going to get something all at once. It’s going to be hard to probably see much of it, before we get it,” Paul said.

Ben Weyl, Daniel Newhauser, Alan K. Ota, Sam Goldfarb and David Harrison contributed to this report.