Even as he and his fellow Republicans tried to chart a path forward, Mr. Boehner said Thursday that he was seeing signs that President Obama and Congressional Democrats failed to realize that Republican gains in Congress resulted from a potent backlash against the Democratic agenda.

“There seems to be some denial on the part of the president and other Democratic leaders of the message that was sent by the American people,” Mr. Boehner said in an interview with ABC News. “When you have the most historic election in over 60, 70 years, you would think the other party would understand that the American people have clearly repudiated the policies they’ve put forward in the last few years.”

Given the chance in the interview to agree with Senator Mitch McConnell, the Republican leader in the Senate, that the party’s goal should be to make Mr. Obama a one-term president, Mr. Boehner responded only that this was Mr. McConnell’s opinion, suggesting that Mr. Boehner was interested in staying out of that particular fight right now.

While the leadership team sees a chance to meld the Tea Party view into the House Republican ideology, there are bound to be conflicts. As the party now controlling the House, Republicans have to produce a budget, spending bills and other legislation that the 40 or so new lawmakers strongly allied to the Tea Party might balk at supporting, leaving the leadership scrambling for votes. Over all, there are at least 80 incoming Republican freshman, and the party is expected to control at least 239 seats. A vote next year on increasing the debt limit  an increase many Tea Party candidates could reject as a fundamental matter of principle  looms as a real test case.

And with the newly energized movement promising to watch closely, the incoming lawmakers will be very leery of seeming to be co-opted by the Congressional establishment, even if it is the leadership of their own party.

Ms. Bachmann’s candidacy suggests that while Republican leaders may face pressure from their Tea Party caucus, it could be manageable. Mr. Hensarling, while not as closely associated with the movement as Ms. Bachmann, is a popular lawmaker who headed the Republican Study Committee, a group of more than 100 conservatives. He has received praise from Tea Party leaders and Republican activists along with his leadership endorsements.

It is not clear if Ms. Bachmann can rally the incoming lawmakers to her side, though she has already won a few public supporters, including Representative John Kline, a fellow Minnesotan, and Representative Steve King, a conservative ally from Iowa.

Mr. Walden predicted that House Republicans would ultimately be able to band together.

“Remember, all of us just stood for election, all of us just faced the same voters in our own states,” he said. “All of us are coming back here understanding that voters want this place to change, and in a meaningful way.”