"No tax increases," Rep. Allen West, R-Fla., said firmly. "That's unacceptable. It's not a good thing to do while we have a fragile recovery."
The tea party is watching, closely.
"It's not that Boehner's an evil person or a bad person," said Judson Phillips, the founder of Tea Party Nation. "I just think he's one of those personalities who wants to be liked. I think he's eager to please and who's going to try to please his liberal friends Barack Obama and Joe Biden. No deal is better than a bad deal."
Phillips said he feared that Boehner was "going to come out in a press conference waving a piece of paper like Neville Chamberlain saying, 'We've got fiscal responsibility in our time.' " Chamberlain, the prime minister of Great Britain, agreed in 1938 to allow Germany to control the Sudetenland in the former Czechoslovakia, and was criticized for appeasing Nazi leader Adolf Hitler.
Boehner still commands sizable Republican support inside and outside Congress.
"Republicans have a lot of confidence in John Boehner," said Rep. Tom Cole, R-Okla., a five-term House veteran. "He has a very good sense of what's necessary, and if John Boehner comes to this conference and asks for their vote, he'll get it." Especially if Cantor and other House GOP leaders are by his side, Cole said.
Grover Norquist, the president of Americans for Tax Reform, an advocacy group that favors a single-rate income tax, said conservative ire at Boehner was misplaced, a legacy of expectations among conservatives when they reached political positions of power.
"People who are disappointed in Boehner think we run the House, the Senate and the White House," he added. "One election doesn't put you in charge of everything."
Carleton College's Schier thought Obama would have an easier time corralling Democrats. "What Obama's got going for him is he let the (Democratic) leaders be in the driver's seat," Schier said.
In 2009-10, Pelosi, then House speaker, and Senate Majority Leader Harry Reid, D-Nev., were largely in charge of strategy on the two key White House initiatives, health care and the economic stimulus. Allowing them to do that, Schier said, "created an enormous amount of good will."
Boehner has a more nuanced challenge. Cantor has solidified his conservative credentials with his rigid, no-tax approach, and by quitting bipartisan debt-reduction talks on June 23.
But Cantor also has signaled a willingness to deal. He participated in those talks for seven weeks, and he developed a working relationship with Vice President Biden. On Wednesday, he opened the door a sliver on taxes by saying he'd consider ending some corporate tax breaks if they were offset by tax cuts.
Ironically, liberal Democrats and conservative Republicans both point to negotiations in April that averted a government shutdown as to why they have reservations about Obama and Boehner sticking to their guns.
"He didn't show me much," said Rep. Jim McDermott, D-Wash., a 12-term veteran. "We don't know where the president's bottom line is, and that means he can be pushed. I want him to stand and say, 'I've been nice to you, I've talked to you, but your demands don't end.' "
Still, the key players remain Obama and Boehner. They played golf June 18, spoke before the president's address to the nation June 22 on Afghanistan, and spoke again last Sunday. During Wednesday's "Twitter town hall," Obama fielded a question about job creation from Boehner.
George Edwards, the editor of Presidential Studies Quarterly, sees compromise ahead.
"The president is a realist," he said, "who knows he has to compromise to achieve change, and to demonstrate competence in governing."
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