Efforts to pass an extension of federal unemployment benefits stalled again Tuesday, as Republicans and Democrats were unable to come up with an agreement on the details of the bill or a process for considering amendments.

Senate Majority Leader Harry ReidHarry Mason ReidDems search for winning playbook Dems face hard choice for State of the Union response The Memo: Immigration battle tests activists’ muscle MORE (D-Nev.) offered Republicans a chance to offer amendments to what has become a Democratic proposal to extend unemployment insurance for 11 months, and pay for that extension with cuts to spending in 2024.

Reid said he would limit amendments to five for each party, and said he would insist on a 60-vote threshold, which guarantees that no GOP amendments would be approved. He then said that in return for allowing amendment votes, Republicans should let the bill be approved or rejected by a simple majority vote, without the need for a 60-vote threshold to end debate.

Reid cast his proposal as one that would help end the gridlock that has plagued the Senate for a few years now.

"We think there should be a new day in the Senate," he said on the floor. "I think that we should start by having a reasonable number of relevant amendments."

But Minority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellSessions: 'We should be like Canada' in how we take in immigrants NSA spying program overcomes key Senate hurdle Overnight Finance: Lawmakers see shutdown odds rising | Trump calls for looser rules for bank loans | Consumer bureau moves to revise payday lending rule | Trump warns China on trade deficit MORE (R-Ky.) said the proposal is a non-starter, precisely because it ensures the failure of Republican proposals to amend the bill. "In other words, it's guaranteed to fix the result in such a way that doesn't give the minority a fair chance," McConnell said.

McConnell countered by asking Democrats to agree to an open amendment process that would let each party alternate between amendment proposals.

After a debate of several minutes, McConnell rejected Reid's proposal, and Reid objected to McConnell's proposal. Reid also objected to other McConnell proposals to bring up a few specific amendments.

The latest speed bump makes it more likely that Congress will adjourn for a week away from Washington without passing an extension of unemployment benefits, and that the Senate may not be in any position to pass anything on its own. House Republicans have indicated little interest in an extension, and have said they would wait to see what the Senate does before considering any next step.

After their debate, McConnell asked for a vote to table Reid's pending motion on the bill, in order to allow consideration of various amendments. But predictably, the Senate voted McConnell's motion down 45-55.

The Senate then held two additional votes that had no real effect other than providing more evidence of the lack of agreement in the Senate.

Members voted 52-48 to end debate on Reid's 11-month jobless benefits proposal, and they voted 55-45 to end debate on the original three-month extension that isn't paid for at all. Both needed 60 votes, and the failure to get those votes means it's back to the drawing board on how to advance the bill.

Just before the debate, Senate Budget Committee ranking member Sen. Jeff SessionsJefferson (Jeff) Beauregard SessionsSessions: 'We should be like Canada' in how we take in immigrants DOJ wades into archdiocese fight for ads on DC buses Overnight Cybersecurity: Bipartisan bill aims to deter election interference | Russian hackers target Senate | House Intel panel subpoenas Bannon | DHS giving 'active defense' cyber tools to private sector MORE (R-Ala.) warned that even if the chamber could get to Reid's proposal, he would raise a budget point of order against it. He said Reid's proposal would violate the budget agreement that Congress agreed to just weeks ago.

"In December, we passed the Murray-Ryan legislation, which did set limits on spending, and the president signed it just two weeks ago," Sessions said on the Senate floor. "And as soon as we waltz into the United States Senate in January of this year, we have a piece of legislation that bursts the budget entirely.

"It is an utter violation of the spending agreements that we agreed to."

Sessions said on Monday that the Reid proposal violates the budget because it pays for a current extension of emergency unemployment benefits by cutting federal spending in 2024. He said that violates the budget agreement because offsetting cuts are supposed to take place within a 10-year budget window, and that delaying cuts until 2024 means "none of it is paid for, effectively."

— This story was updated at 3:45 p.m. and again at 4:28 p.m.