The idea has plenty of skeptics, and the White House regards it frostily. But it illustrates the wide range of early negotiating positions being staked out by Republicans and Democrats as lawmakers gathered Tuesday for their first postelection talks on how to avoid the looming package of steep tax hikes and program cuts.

Just as brazen, in the eyes of many Democrats, is the GOP leaders’ continued insistence on protecting tax cuts for the rich. President Barack Obama just won re-election, campaigning on a vow to end those breaks.

Democrats and Republicans appear heading toward another round of brinkmanship that will test who blinks first on questions of major importance. It’s a dance that has infuriated many Americans, shaken financial markets and drawn ridicule from foreign commentators.

In late 2010, after big GOP midterm election wins, Obama backed off his pledge to raise taxes on the rich. In the summer of 2011, House Republicans pushed Congress within a hair of refusing to raise the debt ceiling, leading to the first-ever downgrade of the government’s credit rating. And last December, it was the Republicans’ turn to blink, yielding to Obama’s demand to extend a payroll tax break.

The “fiscal cliff” deadline comes in seven weeks. One provision: Unless Congress acts, all Bush-era tax cuts would expire, raising 2013 tax bills for most Americans. Obama wants to end those tax cuts only for households making more than $250,000 a year. Republicans insist on no tax rate increases anywhere.

If the “fiscal cliff” takes effect, congressional Republicans would feel pressure to give ground in several areas to achieve their top goal: restoring tax cuts for as many people as possible. That’s why Sen. Patty Murray, D-Wash., and other Democrats have said their party’s leaders should seriously consider letting the Jan. 1 deadline pass and then negotiate with Republicans under sharply different circumstances. Some or most of any new agreements could be made retroactive to Jan. 1, they say.

If Republicans refuse to let tax cuts expire for the wealthy, Murray told ABC’s “This Week,” ”we will reach a point at the end of this year where all the tax cuts expire and we’ll start over next year. And whatever we do will be a tax cut for whatever package we put together. That may be the way to get past this.”

Murray’s allies say voters would blame Republicans for refusing to yield, especially on tax rates, given that Obama won re-election. A recent Pew Research poll supports that view. More than half of the respondents said they would chiefly blame congressional Republicans if there’s no compromise on the fiscal cliff; 29 percent would blame Obama.

It’s questionable whether Obama and Congress’ Democratic leaders would let the government go over the fiscal cliff. Numerous financial analysts say the event would frighten markets, alarm employers and probably trigger a new recession.

However, there’s a school of thought that the cliff is actually a slope, and the economy could withstand the effects of the automatic spending cuts and the renewal of Clinton-era tax rates for at least a few weeks to give time for negotiations to continue. Liberals note that tax rate increases would be felt gradually.

“In the first paycheck of the year, people will see that their withholding is up, but it’s not the like the whole amount of their tax bill for the course of the year takes place in their first paycheck. It happens gradually,” said Chad Stone, an economist with the liberal Center on Budget and Policy Priorities.

The second part of the cliff package includes across-the-board spending cuts of $109 billion a year, split equally between military and domestic programs and known in Washington-speak as a sequester.

Some budget experts say the spending cuts would phase in gradually. Also, Social Security, Medicare and food stamps are exempt. And agency fiscal chiefs have flexibility to mitigate the effects of the sequester.

But such tools are limited. They might buy only a little time before the spending cuts begin to bite harshly, requiring agencies to furlough employees and causing delays in awarding government contracts.

Many say even talk of going over the cliff is sheer folly.

“You’re going to have big financial market repercussions to this,” warned economist Douglas Holtz-Eakin, a former director of the Congressional Budget Office. “Those sorts of confidence measures you don’t control — and they happen abruptly.”

House Minority Leader Nancy Pelosi, D-Calif., showed no interest in challenging the fiscal cliff. “I want you to be disabused of any notion that there is any widespread thought that it would be a good thing, for our country, for us to go over the cliff,” she told reporters Tuesday.

Some Democrats think Republicans are ready to bargain anyway.

“Republicans have a pretty good track record of not blinking,” said Jim Kessler, co-founder of the centrist-Democratic group Third Way. “But they had a bright white light shine in their eyes on Election Day.”

Third Way is floating a possible compromise, designed to raise $1.3 trillion in new revenue over 10 years without changing the Bush-era income tax rates. It would cap itemized tax deductions at $35,000. Charitable deductions, however, would be exempt, a nod to the powerful lobbies of universities and other charity beneficiaries.

The plan also would move upwardly mobile earners into higher tax brackets more quickly. It would reinstate the 2009 estate tax exclusion to $3.5 million, with a tax rate of 45 percent for values above that threshold. And it would raise the tax rate for capital gains and dividends by 5 percentage points, to 23.8 percent.

“Nearly all revenue from this package comes from upper income earners,” Kessler said. His group would prefer to raise tax rates on the wealthiest, he said. But the compromise plan gives Republicans a break on that contentious issue.

Also embroiled in the end-of-year negotiations is the Alternative Minimum Tax, which Congress routinely adjusts to prevent big tax hikes on millions. If Congress fails to act by Dec. 31, an additional 28 million middle-income families would be hit with a large and unexpected tax increase when they file their 2012 returns next spring, the IRS says. Also, the annual AMT “patch” usually includes a rule that affects how tax credits are calculated for about 60 million taxpayers. Those taxpayers — about half of all individual filers — would have to wait until at least the end of March to file their returns while the IRS reworks its systems to account for the existing AMT patch expiring, the agency said.

White House spokesman Jay Carney said Obama hopes for a big bipartisan compromise that will include spending cuts, revenue increases and other features to avert the fiscal cliff. Obama has made it clear, Carney said, “that he is not wedded to every aspect of his plan, and that he understands that in order to reach an agreement, everyone needs to compromise, and that compromise should not be a dirty word in Washington.”