WASHINGTON — The top Senate negotiators on the effort to prevent the government from going over the “fiscal cliff” offered a pessimistic assessment Sunday, barely 24 hours before a deadline to avert tax hikes on virtually every American worker. But negotiations continued, with Vice President Joe Biden taking on a new role.

With the two sides differing on the income threshold for higher tax rates and how to deal with inheritance taxes, among other issues, talks between Senate Majority Leader Harry Reid, D-Nev., and Senate Republican leader Mitch McConnell appeared to have broken down. A McConnell spokesman said the Kentucky Republican reached out to Biden, a longtime friend, in hopes of breaking the impasse.

Republicans withdrew a long-discussed proposal to slow future cost-of-living increases for Social Security recipients as part of a compromise to avoid the cliff.

Democrats said that proposal had put a damper on the talks, and Republican senators emerging from a closed-door GOP meeting said it is no longer part of the equation.

Aides said the two sides remained at odds over the income threshold for higher tax rates, tax levels on large estates and whether Democratic demands for new money to prevent a cut in Medicare payments to doctors and renew jobless benefits for the long-term unemployed should be financed with cuts elsewhere in the budget. The aides demanded anonymity because of the sensitivity of the negotiations.

At stake are sweeping tax hikes and across-the-board spending cuts set to take effect at the turn of the year. Taken together, they’ve been dubbed the fiscal cliff, and economists warn the one-two punch — which leaders in both parties have said they want to avoid — could send the still-fragile economy back into recession.

Reid said he’s been in frequent contact with President Barack Obama, who in a televised interview blamed Republicans for putting the nation’s shaky economy at risk.

“We have been talking to the Republicans ever since the election was over,” Obama said in the interview that was taped Saturday and aired Sunday on NBC’s “Meet the Press.” ‘’They have had trouble saying yes to a number of repeated offers.”

“The mood is discouraged,” said Sen. Joe Lieberman, a Connecticut independent who caucuses with Democrats. He said he would be shocked if there was a deal Sunday. “The parties are much further apart than I hoped they’d be by now.”

The pessimistic turn came as the House and Senate returned to the Capitol for a rare Sunday session. Reid and McConnell had hoped to have a blueprint to present to their rank and file by mid-afternoon.

“I’m concerned with the lack of urgency here. There’s far too much at stake,” McConnell said. “There is no single issue that remains an impossible sticking point — the sticking point appears to be a willingness, an interest or courage to close the deal.”

Reid said he is not “overly optimistic but I am cautiously optimistic,” but reiterated that any agreement would not include the less generous inflation adjustment for Social Security.

“We’re willing to make difficult concessions as part of a balanced, comprehensive agreement, but we’ll not agree to cut Social Security benefits as part of a small or short-term agreement,” Reid said.

McConnell and Reid were hoping for a deal that would prevent higher taxes for most Americans while letting rates rise at higher income levels, although the precise point at which that would occur was a major sticking point.

Obama had wanted to raise the tax rate on individuals making more than $200,000 a year and families making more than $250,000 from 35 percent to 39.6 percent. In talks with Republican House Speaker John Boehner, he offered to raise that threshold to $400,000.

The estate tax issue was particularly tricky since several Democrats, including veterans like Max Baucus of Montana, disagree with Obama’s proposal to increase the top estate tax rate from 35 percent to 45 percent.

Republicans said Democrats pressed to turn off more than $200 billion in the across-the-board spending cuts over the coming two years.

This so-called sequester is the punishment for last year’s deficit “supercommittee” to strike a deal.

Hopes for blocking across-the-board spending cuts were fading and Obama’s proposal to renew the 2-percentage-point payroll tax cut wasn’t even part of the discussion.

Obama pressed lawmakers to start where both sides say they agree — sparing middle-class families from looming tax hikes.

“If we can get that done, that takes a big bite out of the fiscal cliff. It avoids the worst outcomes. And we’re then going to have some tough negotiations in terms of how we continue to reduce the deficit, grow the economy, create jobs,” Obama said in the NBC interview.