Lawmakers on Thursday gave themselves a last chance to prevent the United States from plunging off a “fiscal cliff” by setting up a late session in Congress a day before taxes are due to rise for most working Americans.

Republican leaders in the House of Representatives told their members to be back in Washington from the Christmas holiday break on Sunday in case they need to vote on budget measures.

That leaves the door open to a last-minute solution to avert big tax hikes due to kick in on January 1 and deep, automatic government spending cuts set to begin on January 2 – together worth $600 billion – that could push the United States back into recession.

But the two political parties remained far apart, particularly over plans to increase taxes on the wealthiest Americans to help close the U.S. budget deficit.

The coming days are likely to see either intense bargaining over numbers, or political theater as each side attempts to avoid blame if a deal looks unlikely. Talks could go down to the wire on New Year’s Eve.

“Hopefully, there is still time for an agreement of some kind that saves the taxpayers from a wholly, wholly preventable economic crisis,” Mitch McConnell, the top Republican in the Democratic-controlled Senate, said on the Senate floor.

McConnell said he was willing to look at any plan by President Barack Obama to avoid the fiscal cliff and a Senate aide said congressional leaders could hold talks with the president on Friday.

The rhetoric was still harsh on Thursday after months of wrangling – much of it along ideological lines – over whether to raise taxes and by how much, as well as how to cut back on government spending.

Senate Majority Leader Harry Reid, the top Democrat in Congress, accused Republican House Speaker John Boehner of running a “dictatorship” by refusing to allow bills he did not like onto the floor of the chamber.