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This is WEEKEND EDITION from NPR News. I'm Scott Simon. A lame-duck Congress headed back to work this week. First on the agenda: preliminary negotiations aimed at keeping the country from sailing off the fiscal cliff; across-the-board tax hikes and deep spending cuts that are set to kick in at year's end. As NPR's David Welna reports, a deal may prove a hard sell on Capitol Hill.

DAVID WELNA, BYLINE: Fresh off his re-election, a politically fortified President Obama summoned the top four congressional leaders to the White House yesterday for the first of what could be many rounds of talks for a deal to avert fiscal calamity. In welcoming the quartet of lawmakers, Mr. Obama struck a conciliatory note.

PRESIDENT BARACK OBAMA: Our challenge is to make sure that, you know, we are able to cooperate together, work together find some common ground, make some tough compromises, build some consensus to do the people's business.

WELNA: The president had already made clear at his news conference earlier this week that he has one bottom line as this high-stakes bargaining begins.

OBAMA: What I have told leaders privately as well as publicly is that we cannot afford to extend the Bush tax cuts for the wealthy.

WELNA: Mr. Obama took that same stance two years ago but ultimately relented. This time, backed by a renewed mandate and polls that support his position, he says that won't happen. And House Speaker John Boehner, who scotched a revenue-raising deal with the president last year, emerged from yesterday's meeting on a very different note.

REPRESENTATIVE JOHN BOEHNER: To show our seriousness we've put revenue on the table as long as it's accompanied by significant spending cuts.

WELNA: Boehner did not spell out just what kind of revenue he's willing to consider. But Democrats from President Obama on down say revenue-raising should start by letting the marginal tax rates for the top two income brackets go back on January first to what they were during the Clinton administration. That's fighting talk for hardline House Republicans; one of them is Georgia's Phil Gingrey.

REPRESENTATIVE PHIL GINGREY: I certainly would not be in favor of any so-called millionaires' tax, whether it was imposed at the $250,000, $500,000, one million, five million level. It's a gimmick and it's not solving the problem.

WELNA: And Kansas freshman House Republican Tim Huelskamp, who just got re-elected promising not to raise anybody's taxes, says a tax hike on the wealthiest won't help the economy.

REPRESENTATIVE TIM HUELSKAMP: It might make people feel better - that's what the president's about, making people feel better - but at the end of the day, it's going to cost us jobs.

WELNA: But there are other Republicans in the House who seem resigned to accommodating a wave of public opinion in favor of taxing the rich more. One of them is another lawmaker from Georgia, Jack Kingston. He is not willing to draw a line when it comes to raising some tax rates.

REPRESENTATIVE JACK KINGSTON: I think that there is flexibility in that, and we maybe can argue about what kind of revenues for this, what kind of revenues for that. You know, we do believe that there's more of a spending problem than a taxing problem, but we're also ready to talk.

WELNA: There's speculation the nearly 30 House Republicans who are either retiring or lost their seats in the election could join Democrats to provide the votes needed for a fiscal package raising taxes on the wealthy. Oklahoma House Republican Tom Cole says such a scenario is unlikely, and what a deal would really need to pass would be Speaker Boehner's blessing.

REPRESENTATIVE TOM COLE: On the other hand, if the president thinks that we're going to cave if the speaker doesn't agree, that's not going to happen. I mean, there will not be some group of 30 or 40 republicans flaking off to vote against the majority of their conference. So, I really do think again, at the end of the day, the negotiation, in terms of the House, is principally between the speaker and the president.

WELNA: It may come down, in the end, to a test of which of those two men now holds the upper hand in this negotiation, and which of them is willing to risk going off the fiscal cliff rather than give in. David Welna, NPR News, the Capitol. Transcript provided by NPR, Copyright NPR.