The US government shutdown will extend into the work week as the Senate appeared to inch closer to ending a partisan stalemate late on Sunday but fell short of agreement.

Senate Majority Leader Mitch McConnell and his Democratic leader Chuck Schumer said negotiations were still under way into the night, with a vote to break a Democratic filibuster on a short-term funding bill scheduled for noon on Monday.

Seeking to win over holdout votes, Mr McConnell pledged on Sunday that the Senate would take up legislation on some top Democratic priorities, including immigration, if they are not already addressed by February 8.

“We have yet to reach an agreement on a path forward,” Mr Schumer said, adding that talks would continue.

Mr McConnell’s commitment follows hours of behind-the-scenes talks between the leaders and rank-and-file politicians over how to end the two-day display of legislative dysfunction. The Senate adjourned without voting on Sunday, guaranteeing the shutdown would continue into a third day.

Budget BattleSenate Majority Leader Mitch McConnell (AP)

Republicans have appeared increasingly confident that Democrats were bearing the brunt of criticism for the shutdown and that they would ultimately buckle. The White House and Republican leaders said they would not negotiate with Democrats on immigration until the government is reopened.

There were indications on Sunday that Democratic resolve was beginning to waver, with growing worries that a prolonged shutdown could prove to be an electoral headache for the party just as they have grown confident about their prospects in November.

Discussions took place in behind closed doors throughout the day with few outward signs of progress, as politicians took turns delivering animated speeches to near empty chambers to explain why the other party is to blame.

As politicians feuded, signs of the shutdown were evident at national parks and in some federal agencies. Social Security and most other safety-net programmes were unaffected by the lapse in federal spending authority. Critical government functions continued, with uniformed service members, health inspectors and law enforcement officers set to work without pay.

Politicians were mindful that the political stakes would soar on Monday morning, when thousands of federal workers would be told to stay home or, in many cases, work without pay. What was still a weekend burst of Washington dysfunction could spiral into a broader crisis with political consequences in November’s midterm elections.

Budget BattleChuck Schumer explains how his negotiations with Donald Trump broke down (AP)

Democrats, who initially dug in on a demand for legislation to protect about 700,000 immigrants who were brought illegally to the country as children, shifted to blame the shutdown on the incompetence of President Donald Trump and the Republican leadership.

Republicans argued that Democrats shuttered the government over “illegal immigration” in a bid to gin up enthusiasm among their base.

Absent a breakthrough, the vote on Monday will prove to be a test of unity and resolve among Democrats. Five Democrats from states won by Mr Trump broke ranks in a vote Friday. The measure gained 50 votes to proceed to 49 against, but 60 were needed to break a Democratic filibuster.

Mr Trump, who regularly disrupted negotiations in recent weeks, had been a relatively subdued player in the weekend debate. He has not appeared in public since Friday afternoon. The White House said he was in regular contact with Republican leaders, but he has not reached out to any Democrats, a White House official said.

On Sunday morning on Twitter, he called on the Republican-controlled Senate to consider deploying the “nuclear option” – changing Senate rules to end the filibuster – and reopen the government with a simple majority.

Mr McConnell has dismissed that option, saying Republicans will welcome the filibuster when they return to being the Senate minority.

Democrats are facing intense pressure from their base to solve the issue over the young immigrants, and they are sceptical of Republicans’ credibility when offering to deal. Whether Mr Trump would back the emerging plan or any later proposal on immigration is an open question. Even if the Senate voted on an immigration proposal, its prospects in the House would be grim.

Furthermore, Democrats view Trump as an infuriating bargaining partner, pointing chiefly to his failed 11th-hour talks with Mr Schumer on Friday. The Democrat says Mr Trump expressed support for a fix for the young immigrants in return for financing for mr Trump’s wall along the US-Mexico border — only to back off hours later. The White House says Mr Schumer and the president never came to terms.

“How can you negotiate with the president under those circumstances where he agrees face to face to move forward with a certain path and then within two hours calls back and pulls the plug?” asked Senator Dick Durbin on ABC’s This Week on Sunday.