For the first time in decades, a bipartisan consensus has emerged in Washington to raise taxes. But negotiators working to avert the year-end “fiscal cliff” remain far apart on crucial details, including how taxes should go up and who should pay more.

Neither side gave ground in an opening round of staff-level talks last week at the Capitol. As President Obama and congressional leaders prepare for a second face-to-face meeting as soon as this week, the divide over taxes presents the biggest obstacle to replacing the heap of abrupt tax hikes and spending cuts, set to hit in January, with a less-traumatic debt-reduction plan.

People in both parties are exploring ideas for bridging the gap. Without a deal on taxes, there is not much hope for agreement on a broader strategy for restraining the national debt that also tackles the skyrocketing cost of federal retirement programs such as Social Security and Medicare.

But with tax rates set to rise automatically in January when the George W. Bush-era tax cuts expire, Democrats say they have little incentive before then to cut a deal that falls short of their revenue goals. That means going over the cliff, at least for a short time, remains a possibility, they say.

“The bottom line is we’re about to have a poker game and it’ll be hard to read” what each side is willing to do, said Kevin Hassett, a senior fellow at the American Enterprise Institute and a former adviser to Republican presidential candidate Mitt Romney.

What going over the 'fiscal cliff' would mean . . .

For now, Democrats are seeking $1.6 trillion in new taxes over the next decade collected from about 3 million families at the pinnacle of the income spectrum — those earning more than $250,000 a year. The Democrats want to start by letting the top two tax rates return to 36 percent and 39.6 percent when the Bush tax cuts expire.

Republicans insist on maintaining the Bush rates, at 33 percent and 35 percent, through 2013. Instead, they want to raise cash by rewriting the tax code to eliminate individual loopholes and deductions, an approach House Speaker John A. Boehner (R-Ohio) argues would be less harmful to businesses and the economy.

It is also more popular, Republicans say. They pointed to a new poll by the Winston Group, a GOP research firm whose president, David Winston, is close to Boehner. Sixty-five percent of those surveyed preferred a deal that wipes out “special interest tax loopholes and deductions commonly used by the wealthy” over an approach that raises tax rates on “Americans earning more than $250,000” on Jan. 1.

GOP negotiators have declined to say how much they are willing to raise, according to people familiar with the talks. In the past, Boehner has proposed $800 billion. But who, in the Republicans’ view, should foot that bill is unclear.

Major deductions, such as breaks for mortgage interest and charitable contributions, disproportionately benefit the wealthy but also reach far into the middle class. Capping all itemized deductions at $17,000, an idea offered by Romney, would affect the wealthy but raise tax bills for nearly 15 percent of families making between $40,000 and $50,000 a year, according to the independent Tax Policy Center.

A proposal by Sen. Bob Corker (R-Tenn.) to cap deductions at $50,000 would come closer to focusing the impact on households earning more than $250,000, but it would also raise less money.

Some Republicans are willing to explicitly tax the rich, but only if the target group is smaller. For example, Sen. Susan Collins (R-Maine) has suggested a 2 percent surtax on millionaires, who make up just 0.3 percent of taxpayers — about 400,000 households. And Collins would exempt small-business owners whose profits are taxed on their personal returns.

“Multimillionaires and billionaires who are not running businesses could pay more of their income to help reduce the $16 trillion federal debt,” Collins said in a statement last week. “But I feel strongly that we must ensure that small-business owners . . . are protected.”

The continuing dispute over taxes contrasts with the bipartisan unity on display Nov. 16 at the White House, when Boehner and Senate Minority Leader Mitch McConnell (R-Ky.) met with Obama and Democrats Harry M. Reid (Nev.), the Senate majority leader, and Nancy Pelosi (Calif.), the House minority leader. Days after an election that returned Obama to the Oval Office and returned the GOP to power in the House, the leaders vowed to work together to avoid the dramatic year-end tax hikes and spending cuts, which threaten to spark a new recession, and adopt a more gradual debt-reduction plan.

Pelosi suggested a Christmas deadline, a sign of optimism that briefly buoyed financial markets. But except for agreeing to pursue a two-step legislative “framework,” the group hammered out no details. That was left to top aides who were instructed to develop an agenda for the leaders’ next meeting, which on Sunday had yet to be scheduled.

The framework calls for an immediate down payment, likely to include tax hikes and spending cuts, along with targets for further tax increases and entitlement cuts to be achieved through a broader debt-reduction effort next year.

Taxes are hardly the only point of contention. In exchange for raising additional revenue, Republicans want cuts to fast-growing federal retirement programs, projected to be the biggest driver of future borrowing. Their opening bid included a demand to apply a less-generous measure of inflation to Social Security, which would slow the rise of benefit payments.

Obama agreed to the idea in talks with Boehner during the summer of 2011. But since the election, liberal groups have mobilized against it and Reid has ruled it out. On Sunday, the No. 2 Senate Democrat, Sen. Richard J. Durbin (Ill.), appeared to endorse Reid’s position, though he argued that Democrats should ignore calls to take Medicare off the table.

“Social Security does not add one penny to our debt — not a penny. It’s a separate funded operation,” Durbin said on ABC’s “This Week with George Stephanopoulos.” “Medicare’s another story — only 12 years of solvency if we do nothing. So those who say, ‘Don’t touch it. Don’t change it,’ are ignoring the obvious.”

Durbin suggested higher payments for “high-income beneficiaries” but expressed concerns about another idea Obama has previously accepted — raising the Medicare eligibility age from 65 to 67.

Sen. Lindsey O. Graham (R-S.C) said on the same show that gradually raising the retirement age — for both Medicare and Social Security — is exactly the kind of “eminently reasonable” entitlement reform Republicans will demand.

“I don’t expect Democrats to go for premium support or a voucher plan,” Graham said, referring to a Medicare proposal championed by Rep. Paul Ryan (R-Wis.). “But I do expect them to adjust these entitlement programs before they bankrupt the country.”

The talks must also address other critical issues, including the federal debt limit, which is set by law at $16.4 trillion. The national debt is approaching $16.3 trillion, and Democrats are hoping Republicans will agree to an increase as part of a fiscal-cliff deal.

No such offer was forthcoming last week, but Republicans, too, are interested in getting the debt limit off their plate and avoiding a repeat of the damaging debt-ceiling standoff that sent congressional approval ratings plummeting in the summer of 2011.

Taxes, however, remain the key to a breakthrough, people in both parties say. Obama has left the door open to a compromise that would raise the top rate for 2013 to something less than 39.6 percent, a move Republicans took as an encouraging sign.

Democrats have continued to press for legislation that extends the Bush cuts for 98 percent of taxpayers and lets the top rates expire. Along with changes to the inheritance tax, the expiration of the Bush tax cuts would generate about $1 trillion over the next decade compared with current policy. The immediate question, in Democrat’s view, is the scope of entitlement cuts Republicans want in exchange for passing such legislation.

Republicans close to the talks say they will not extend the Bush rates only for some taxpayers. Instead, they have been scrambling to come up with alternatives for raising the same amount of money — around $50 billion in 2013 — from the same group of people.

Among the options floated by Republican tax aides is a “bubble tax,” which would eliminate the benefit of the lower tax brackets for taxpayers over a certain income level. (Currently, for instance, all taxpayers benefit from a 10 percent tax rate on the first $8,700 of income regardless of their total income.) In a recent report, the bipartisan Committee for a Responsible Federal Budget offered other ideas, including a $25,000 cap on itemized deductions for taxpayers who earn more than $250,000 a year.

Targeting deductions now, however, could limit the amount Democrats raise later through rewriting the tax code. Obama, after all, has proposed his own limit on itemized deductions, which would raise an additional $600 billion over the next decade on top of the money to be gained from increasing tax rates.

“A much wiser course would be to let the Bush tax cuts sunset,” said Chuck Marr, a tax expert at the left-leaning Center on Budget and Policy Priorities. “You’d be locking in nearly $1 trillion in 10-year savings. And then one can start talking about reforming” deductions.

Zachary A. Goldfarb contributed to this report.