Rep. Michele Bachmann, the firebrand congresswoman from Minnesota who formed the Tea Party caucus, announced her intentions Wednesday to run for the GOP conference chair, the fourth top leadership position in the party.
Bachmann's Facebook announcement sets up the first real battle between the GOP establishment and Tea Party supporters. She will be competing against Rep. Jeb Hensarling, R-Texas, a favorite of the Republican establishment.
Dick Armey, former House majority leader and founder of the conservative, Tea Party support group called FreedomWorks, dismissed the idea of any fractions within the GOP.
"What you see with this leadership team is quiet competence," Armey said on "Good Morning America." Boehner, set to be the new speaker of the House, has the "proven ability to work with even the most diligent people on the other side."
As minority leader, Boehner was outspoken and defiant. He famously yelled "Hell no they can't" on the House floor during a health care debate.
The soon-to-be House speaker struck a more somber tone Wednesday, however, warning that now is no time for celebration and that the winners have their work cut out ahead. He also said the Democratic agenda may have to be retooled.
"Our job is to listen to the American people and follow the will of the American people," he said. "We've got a big job ahead of us, and that's why you see us roll up our sleeves and go to work today."
Democrats clearly have reservations about which issues the two parties can compromise. Many Republicans who were swept into power by Tea Party fervor have vowed a repeal of the health care bill. Others disagree vehemently with Democrats' budget proposal, which could create a stalemate next spring when the two sides join heads to formulate a plan.
There's a "really, really new reality in Washington," Democratic strategist James Carville said on "GMA" today.
The two parties can start out by compromising on small bills such as eliminating earmarks and pork barrel spending -- a Congressional tactic both Obama and Boehner have decried -- but "it's not going to be a whole lot of common ground," he said.
The future of the health care bill is also up in the air.
Republicans, including Leader McConnell, are insisting that parts of it should be repealed. But the president, who has veto power, is unlikely to support such a move.
"On health care, that means we can -- and should -- propose and vote on straight repeal, repeatedly," McConnell will say in a speech today, according to prepared remarks. "But we can't expect the president to sign it. So we'll also have to work, in the House, on denying funds for implementation, and, in the Senate, on votes against its most egregious provisions."
ABC News' Jonathan Karl and Jake Tapper contributed to this report.