After Mitt Romney's defeat on Tuesday, John Boehner is the undisputed leader of the Republican Party.

Pity him.

President Obama's re-election and the Democrats' successful defense of their Senate majority have put the House speaker in a vise. Squeezing him on one side are the tea party conservatives and their ilk, dominant in the House Republican majority, who say Romney lost because he was too accommodating and moderate. Squeezing him on the other side is a Democratic president who campaigned for the rich to pay a higher share of taxes.

Boehner's first instinct on Tuesday night was to side with his House firebrands. "While others chose inaction," he said at a Republican National Committee event, "we offered solutions."

Americans, he said, "responded by renewing our House Republican majority. With this vote, the American people have also made clear that there's no mandate for raising tax rates."

After sleeping on it, Boehner appeared at the Capitol on Wednesday and offered a dramatically different message: He proposed, albeit in a noncommittal way, putting tax increases on the table.

"Mr. President, this is your moment," he said into the cameras, reading, sometimes with difficulty, from a teleprompter. "We're ready to be led, not as Democrats or Republicans, but as Americans. ... We want you to succeed. Let's challenge ourselves to find the common ground that has eluded us."

Boehner left himself sufficient wiggle room, saying, "We're willing to accept new revenue under the right conditions" -- which keeps alive the possibility that the revenue would come only from economic growth (the old Republican position) and not from a higher tax burden.

Still, Boehner's new tone was starkly different from the one set two years ago by Senate Minority Leader Mitch McConnell, R-Ky., who declared that "the single most important thing we want to achieve is for President Obama to be a one-term president." McConnell continued that approach after Tuesday's election, saying, "The voters have not endorsed the failures or excesses of the president's first term."

But the voters denied McConnell his top priority. And exit polls Tuesday showed that a majority of them favored higher taxes on income over $250,000, as Obama has proposed -- something Boehner's Democratic counterpart in the Senate, Majority Leader Harry Reid (Nev.), made sure to point out in a news conference before the speaker's appearance. The voters, Reid said, "want a balanced approach ... and taxes are a part of that."

But Boehner's talk of common ground is likely to enrage the no-compromise wing of his House Republicans, who live in fear of the tea party, Grover Norquist, the Club for Growth and other enforcers of conservative orthodoxy. And tea party leaders have convinced themselves that Romney lost because he wasn't conservative enough. The Tea Party Patriots, for example, attributed Romney's defeat to his being a "weak moderate candidate, handpicked by the Beltway elites and country-club establishment."

More likely, the tea party itself bears the blame for Romney's loss -- just as losses by far-right candidates kept Republicans from taking over the Senate.

To survive conservative primary challenges from Newt Gingrich, Rick Santorum, Rick Perry and others, Romney had to take positions that ultimately doomed him in the general election. His tough-on-immigration stance, in particular, helps explain his loss of more than 70 percent of the Latino vote, which sealed his defeat.

Boehner knows this, of course, and that is why he was so careful when he made his remarks Wednesday afternoon, taking the rare precaution of using a teleprompter. He left without answering questions, and when reporters shouted queries at him, he only smiled.

"The American people have spoken," Boehner said somberly, his eyes glistening. "If there's a mandate in yesterday's results, it's a mandate for us to find a way to work together."

Although he was vague about what he was offering, his bargaining position was very different from 18 months ago, when he went to the Economic Club of New York and pronounced tax increases "off the table." This time, he outlined the general framework of a grand bargain: "In order to garner Republican support for new revenue, the president must be willing to reduce spending and shore up entitlement programs."

Boehner chose to make his post-election speech in the Capitol's Rayburn room, named for Sam Rayburn, the late House speaker who is credited with saying: "Any jackass can kick down a barn, but it takes a carpenter to build one."

Boehner sounds as though he's ready to pick up hammer and nail. But will his fellow Republicans stop kicking?