Negotiations to extend emergency benefits for the long-term jobless deadlocked in the Senate on Tuesday. That leaves more than 1.3 million people without federal unemployment aid at least until late January, when lawmakers are likely to resume consideration of the legislation.

Democrats and Republicans accused each other of bad-faith negotiations, and by late Tuesday they had rejected each other’s latest proposal. After parliamentary votes to advance the legislation failed, senators moved on to debating the bill to fund government agencies through 2014. Congress leaves town Friday for a weeklong recess and will return Jan. 27, the earliest that new talks could provide a breakthrough on an unemployment plan.

“There may be a faint detection of a pulse somewhere, but we’ve got a patient in very critical condition now,” said Sen. Daniel Coats (R-Ind.), one of nine GOP senators who had been promoting an alternative bill.

Sen. Jack Reed (D-R.I.), the lead sponsor of the legislation, told reporters, “We’re not giving up.”

The law providing federal assistance to unemployed workers who go past the usual allotment of 26 weeks of jobless aid expired in late December. The previous law allowed for up to an additional 47 weeks for the unemployed in states such as Nevada and Rhode Island, tied for the nation’s highest jobless rate, at 9 percent.

View Graphic Who are the long-term unemployed?

Majority Leader Harry M. Reid (D-Nev.) set up the unemployment assistance debate as the Senate’s first legislative business in the new year. Since Jan. 6, most senators have agreed on the need to extend benefits for the jobless who have lost federal unemployment assistance — 1.3 million and counting — but they have fought over proposals to find offsetting savings to assure the program would not increase the deficit.

The short-term impact of the stalemate is to deny aid to a subset of the labor force that economists now consider the most troubling hindrance to a full recovery: the long-term unemployed. The longer-term hit, if there is no resolution, is that the broader national economy will lose the stimulative boost of more than $25 billion in consumer spending that the unemployment benefits could provide over the next year.

Despite suggestions over the past week that a deal was emerging, the two sides were never particularly close — certainly not on a plan that would have won enough support in the House, where conservatives have shown little appetite for the various proposals.

The latest offer came late Monday from a group of nine Republicans proposing a three-month extension of the emergency unemployment program. The group wanted it paired with a proposal to nix a reduction in cost-of- living adjustments to the pensions of retired members of the military who are still of working age.

With a total price tag of about $12 billion, the Republican proposal offered savings by eliminating the ability of the unemployed to receive both federal disability payments and jobless aid. Also included was a provision to extend portions of automatic spending cuts but walling off the military and Medicare providers to increased cuts.

The proposal was similar in some respects to Reed’s latest, but he suggested it was also “robbing Peter to pay Peter” because some of the proposed spending cuts would hit programs that would assist the poor.

“That was never going to have a chance on our side,” Sen. Charles E. Schumer (N.Y.), the No. 3 Democrat in the chamber, told reporters.

That came after Republicans had rejected a Democratic proposal to extend the unemployment plan until mid-November with a different extension of the automatic cuts, known as sequestration. Republicans said those proposed cuts did not materialize until 2024, too far off to even be properly scored by the Congressional Budget Office.

After rejecting each side’s substantive proposals, Democrats and Republicans devolved into arguing over procedural steps. Democrats accused Republicans of trying to propose amendments designed to hurt politically, without any guarantee the overall issue would win final approval.

GOP senators accused Reid of trying to navigate the debate into failure so Democratic allies could attack Republicans as not caring about the unemployed. At first Reid did not allow amendments to the initial proposal, and when he did allow consideration this week, Republicans said they were backed into a corner with an accompanying demand to give up their right to filibuster the underlying Democratic proposal.

Now, each side is waiting for the other to make the next offer. “The ball’s in their court,” Coats said.