This analysis is by Charles Babington of The Associated Press.

Democrats feel they're closer than ever in their long-running bid to paint Republicans as being much more eager to cut taxes for the rich than for the working class.

But public contempt for Congress is so rampant that the effort may fade away in a pox-on-all-their-hou​ses fog. If that happens, President Barack Obama and congressional Democrats could lose a political edge as they head into the 2012 elections with a struggling economy.

Democratic strategists say Republicans are blundering by refusing to extend a payroll tax cut, even after the Senate overwhelmingly approved a temporary compromise Saturday. GOP lawmakers previously fought hard to extend Bush-era income tax cuts for everyone, including the wealthiest.

"This is a rare moment when the public is with the Democrats on a tax issue, and against the Republicans," said Sen. Charles Schumer, D-N.Y.

Some conservative bloggers have urged Republican lawmakers to embrace the payroll tax cut extension, saying the GOP is identified with tax cuts.

(Post continues after video.)

Even if the impasse leads to a tax increase on wage earners in two weeks, Democrats will have a hard time convincing voters that they're the good guys and Republicans are the bad guys, said GOP strategist Rich Galen. Americans are so sick of congressional squabbling, he said, "they have tuned that kind of stuff out. I don't think anybody believes any of them anymore."

For the past few years, Republicans have fought hard to extend the Bush-era income tax cuts for everyone. Obama unsuccessfully tried to end those tax cuts for high-income people on schedule.

Republicans have taken a different tone on the payroll tax cut, which steers more proportional benefits to low- and middle-income workers.

At Obama's urging, Congress agreed last year to reduce the tax that nearly all wage earners pay toward Social Security. Long set at 6.2%, the levy was temporarily lowered to 4.2% for 2011. (A separate 6.2% paid by employers was unchanged).

Citing the bad economy, Obama said he wants to extend the payroll tax reduction for another year: all of 2012. Many GOP leaders balked, demanding concessions in return. Among other things, Republicans said a payroll tax cut must be offset by federal spending reductions elsewhere. They did not apply that condition when extending the Bush-era income tax cuts.

With the payroll tax scheduled to return to 6.2% on Jan. 1, the GOP-controlled House and Democratic-controlle​d Senate have been unable to reach an accord. The Senate approved a two-month extension of the lower rate last weekend and adjourned for the year, planning to revisit the matter in February.

House Speaker John Boehner, R-Ohio, said Monday the House would reject the Senate plan and call on senators to return to the negotiating table. Senate Democratic leaders signaled no plans to do so.

House Republicans say it's foolish and cowardly to extend the payroll tax cut for only two months. Ed Goeas, a GOP pollster who has worked in presidential and congressional campaigns, predicts the public eventually will agree.

"Do the Democrats have a quick sound bite?" Goeas asked. "Absolutely." But voters see short-term fixes as gimmicks, he said, "and gimmicks turn them off."

Schumer said it's laughable for Republican lawmakers to say a two-month tax extension isn't enough after they spent months resisting any tax extension at all. "The American people are seeing through this," he said.

Numerous GOP lawmakers spoke against a payroll tax extension last summer and fall, before the debate reached a boil. "The payroll tax holiday has not stimulated job creation," Jon Kyl of Arizona, the Senate's second-ranking GOP leader, told "Fox News Sunday" on Nov. 27.

A spokesman for House Majority Leader Eric Cantor, R-Va., said in August that Cantor has never believed a one-year tax reduction "is the best way to grow the economy."

Schumer said Democrats made numerous concessions in seeking Republican support for another year with a 4.2% payroll tax rate. They dropped Obama's bid for an even deeper cut, dropped Obama's bid for a surtax on millionaires to offset the payroll reduction and agreed to require Obama to make a swift decision on a proposed oil pipeline, which environmental groups oppose.

"They won't take 'yes' for an answer," Schumer said.

Obama is using the tax issue to portray Republicans as being far more keen on protecting tax cuts for the rich than for low- and middle-income people.

"Tonight, Senate Republicans chose to raise taxes on nearly 160 million hard-working Americans because they refused to ask a few hundred thousand millionaires and billionaires to pay their fair share," Obama said Dec. 1, after GOP senators and three Democrats voted to block his proposed surtax on the very wealthy.

The issue has split the GOP presidential field. Former Massachusetts Gov. Mitt Romney, former House Speaker Newt Gingrich and Rep. Ron Paul, R-Texas, have called for extending the payroll tax for a year. Opposing the idea are Texas Gov. Rick Perry, former Sen. Rick Santorum of Pennsylvania, and Rep. Michele Bachmann, R-Minn.

Last summer, Gingrich predicted that Republicans would fall under increasing pressure to extend the payroll tax cut. If they refuse, he said, "we're going to end up in a position where we're going to raise taxes on the lowest-income Americans the day they go to work."

Republicans say income tax increases on upper-income people hurt job creation, but payroll tax cuts do little to spur economic growth. Many Democrats disagree. They cite economists who say an extended payroll tax reduction would lead to more consumer spending and boost the economy, at least a little.

Obama spokesman Jay Carney told reporters Monday: "I think Americans who are paying attention to this must be pulling their hair out when they look at the House now refusing to do what the Senate did."

Copyright 2011 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.

More from MSN Money:

• 58% of Americans want payroll tax cut extended
• Study: Gingrich plan would aid rich, add to deficit
• Not in the top 1%? Just where in the 99% are you?
• Does Cain's 9-9-9 tax plan add up?
• Is it time to look at oil company tax breaks?
• 7 tax reasons not to get married