With House of Representatives Republicans under attack from friends and foes, Democrats held out for victory in a fight over extending a payroll tax cut for millions of workers that is set to expire at year's end.

He (House Speaker John Boehner) will cave, a senior Democratic aide flatly predicted, expressing the sentiment and hopes of many in Congress on both sides of the political aisle.

In public statements so far, House Republicans have shown no willingness to give up their demand for a new round of last-minute negotiations on the tax cut.

President Barack Obama on Wednesday tried to move things along, though, when he telephoned Boehner, the leading Republican. The White House said the president offered to help work out a year-long payroll tax cut that both sides say they want, but so far have been unable to figure out how to pay for.

But first, Obama and his fellow Democrats said that the Republican-controlled House must agree to the two-month extension that overwhelmingly passed the Senate on Saturday. Doing so, Democrats argued, would ensure a seamless continuation of a 4.2 percent payroll tax rate and stall the 6.2 percent rate that would kick in on January 1 without the extension.

A senior Senate Republican aide, saying the flap was hurting his party politically, speculated that Boehner could orchestrate some minor changes to the Senate-passed bill, pass it in the House and send it to the Senate for final approval.

At stake is a year-old tax cut for 160 million American workers that if left to expire would significantly cut into U.S. economic growth, according to some economists and businesses. The current lower tax rate puts about $1,000 in additional spending money in the average worker's hands.

Boehner's Republicans were feeling heat not just from Democrats. All week long, some Senate Republicans have lashed out at the House's refusal to accept a carefully negotiated Senate bill.

Meanwhile, the editorial page of the Wall Street Journal, usually a safe harbor for conservative Republicans, wrote of a Republican fiasco. The newspaper called on Boehner's troops to cut their losses having thoroughly botched the politics.

Republican Senator John McCain, his party's 2008 presidential candidate, agreed. WSJ is right on the mark here, he wrote in a tweet.

Another senior Republican aide fretted that this end-of-year fight was costing Republicans our brand as being for limited government and tax cuts, and we're allowing Democrats to turn it on its head. The aide added, The longer House Republicans drag this out, the worse it gets for Republicans.

The fierce fighting in Congress, which has raged all year on budget and tax matters, already has rattled investors who are looking to Washington to effectively deal with a rapidly rising national debt that has topped $15 trillion.

The lack of political cooperation in Washington led one agency, Standard and Poor's, to downgrade the federal government's stellar AAA credit rating last August.

If a deal is reached on a short-term payroll and unemployment benefits extension, tough negotiations are expected early next year on continuing the measures through the rest of 2012. Those talks would occur against the backdrop of presidential and congressional election campaigns that are intensifying, further complicating the negotiators' work.