Republican chairmanship term limits are bringing a dilemma for the party in the next Congress: whether to break the rules for a promising intellectual leader of the party while denying his ambitious colleagues the same opportunity.

Rep. Paul Ryan, chairman of the House Budget Committee, is term-limited at the end of this Congress, having ascended to the ranking member position on the panel in 2006. Republicans count time served as chairman and ranking member toward term limits.

GOP officials and aides said they expect significant pressure for the Steering Committee to grant Ryan, the public face of House Republicans on budget and economic issues, a waiver from the six-year term limits rule, allowing him to stay on.

That’s especially so because there’s no other obvious place for the Wisconsin Republican to ascend to in the House.

Ryan’s “dream” is to one day become chairman of the Ways and Means Committee, sources said, but Rep. Dave Camp (R-Mich.), chairman of the tax panel, has until 2014 before he faces term limits.

While there is speculation that presumptive GOP presidential nominee Mitt Romney could select Ryan for the vice presidential nomination or to head the Treasury Department, absent that, many Republicans expect him to stay at the Budget Committee for another two years before making a bid for the Ways and Means gavel.

“If Ryan remains in the House, the best thing for House Republicans and the most natural progression for him would be to remain Budget chairman for one more term and then become chairman of the Ways and Means Committee,” said a Republican official familiar with the situation.

But Republicans have been stingy about issuing waivers for chairmanship term limits since the rule was implemented in 1995. And a waiver for Ryan could roil other GOP chairmen who would like to stay on. A spokesman for Ryan did not return a request for comment.

Rep. John Mica, chairman of the Transportation and Infrastructure Committee, is also term-limited at the end of this Congress.

The Florida Republican recently said he is seeking a waiver. He faces a tough primary against freshman Rep. Sandy Adams and has been touting his seniority and sway to voters.

In an interview with Roll Call, Mica broadened the horizons of his ambitions, predicting he would get “either a full committee [chairmanship] or a major leadership position in the House.”

According to Mica, the question of waivers and chairmanships is still wide open.

“One, no one even knows who the leadership is. I just read in the paper today … one of the stories is who is going to succeed [National Republican Congressional Committee Chairman Pete Sessions]. That position has a major impact … and we don’t know who will be there. So, if someone has a crystal ball or they’ve been given in a Chinese fortune cookie how this will happen, I would like to know it,” Mica said.

A wide array of Republican sources were dismissive of Mica obtaining a waiver to stay on as chairman.

If the question is the transportation panel, a waiver for Mica could trigger the wrath of Rep. Bill Shuster (R-Pa.), for whom the term-limits issue is personal.

In 2001, Shuster’s father, former Rep. Bud Shuster (R-Pa.), was denied a waiver to stay on as chairman of the Transportation and Infrastructure Committee.

Republicans faced a similar issue then as they do now. The late Rep. Henry Hyde (R-Ill.) wished to stay on as Judiciary chairman. He had a high profile thanks to his role in the impeachment of President Bill Clinton, and he lobbied then-Speaker Dennis Hastert (R-Ill.) and the Steering Committee for a waiver.

But then-Majority Leader Dick Armey (R-Texas) pushed against a waiver for Hyde, fearing it would open the door for a waiver for others, including Bud Shuster.

In the end, no one received a waiver, and Shuster resigned.

Now, more than 11 years later, Bill Shuster is in a position to make a play for Mica’s gavel.

“Committee Chairmanships are decisions for the Steering Committee and Leadership to consider,” Shuster said in a statement. “Right now, my focus is on working with Chairman Mica and the House conferees to pass a strong transportation bill.”

Three other GOP chairmen face term limits at the end of this Congress: Judiciary Chairman Lamar Smith (Texas), Financial Services Chairman Spencer Bachus (Ala.) and Science, Space and Technology Chairman Ralph Hall (Texas).

None is expected to push for waivers.

The list of Republicans who have obtained waivers is short.

Ohio Gov. and former Rep. John Kasich was granted a waiver in 1999 to stay on as Budget chairman. Former Rep. Porter Goss (Fla.) was granted a waiver to remain Intelligence chairman in 2004.

Rep. David Dreier (R-Calif.) became chairman of the Rules Committee in 1999, but that slot, viewed as an extension of the leadership team, is appointed by the Speaker rather than elected by the Steering Committee.

The Steering Committee, composed of a mix of leadership, committee chairmen, rank and file, and freshmen, will decide the fates of Ryan, Mica and the other chairmen. Speaker John Boehner (Ohio) gets four votes and Majority Leader Eric Cantor (Va.) has two. The other members get one vote. A Boehner spokesman declined to comment.

Joshua Miller and Ryan Kelly contributed to this report.