WASHINGTON -- The White House and congressional leaders worked overtime Sunday to ward off tax increases set to kick in for most Americans, with Republican leaders signaling a grudging acceptance that some taxes will go up and the two parties narrowing their differences over who should pay more.

After a mid-day stumble, the two sides worked in private, debating a slimmed-down package that would increase taxes for top wage earners – perhaps hitting incomes somewhere between $360,000 and $450,000 - while preserving income taxes breaks for tens of millions of other Americans.

“There is still significant distance between the two sides, but negotiations continue,” Senate Majority Leader Harry Reid, D-Nev., said on the Senate floor following a closed door meeting with fellow Democrats. “There’s still time left to reach an agreement, and we intend to continue negotiations.”

The Senate and House scrapped plans to cast votes Sunday night. They will return Monday, the last possible day to vote before all of the Bush-era tax cuts expire at the end of the day.

The signs of progress late Sunday came after a day of drama in which talks appeared to hit an impasse, Reid suggested he could not get the White House to sign off on a counter-offer, and Senate Minority Leader Mitch McConnell, R-Ky., made an open appeal to old Senate colleague Joe Biden, now the vice president, to help get talks moving again.

The talks between Reid and McConnell had broken down early Sunday over a Republican proposal to curb the growth of benefits under entitlement programs such as Social Security and Medicare. Unable to get a response from Reid, McConnell turned to Biden, who helped broker deals over tax cuts in 2010 and the debt ceiling in 2011. Biden and McConnell spoke more than three times by phone Sunday, aides said. Republicans eventually dropped their proposal for entitlement changes as part of this potential deal.

Unless Congress acts, the country faces a one-two dose of automatic tax increases and spending cuts, affecting nearly every taxpayer and many government programs. The tax increases would come as all of the Bush era tax cuts expire at 12:01 am Tuesday. The across-the-board spending cuts kick in days later, part of a doomsday package Congress enacted thinking – falsely – that it would force members to enact more carefully designed cuts.

Democrats proposed extending only those Bush era tax cuts on individual income below $200,000 and family income below $250,000, raising taxes on income above that. Republicans had been pushing to extend all of the tax cuts.

But late Sunday afternoon, Republicans offered to sign off on raising taxes on individuals earning more than $450,000 while Democrats countered with $360,000, several senators said.

Other issues being considered as part of a possible package included extending unemployment benefits for 2 million Americans, preventing about 30 million Americans from having to pay the alternative minimum tax, keeping Medicare payments to doctors at the current rate and extending tax breaks offered to companies and individuals, according to a congressional aide familiar with the talks but not authorized to speak publicly.

The two sides also continued to debate the estate tax. Democrats want to raise the tax from 35 percent to 45 percent and apply it to estates above $3.5 million, rather than the current $5.2 million. Republicans want current rates to prevail.