A compromise on immigration means a vote to reopen the US Government has passed - but it's unclear exactly what that compromise will entail.

Senators voted 81-18 in favour of a funding bill.

Republicans and Democrats had spent the weekend trying to strike a deal, only to go home for the night short of an agreement.

The US government cannot fully operate without funding bills that are voted in congress regularly.

Washington has been hampered by frequent threats of a shutdown in recent years as the two parties fight over spending, immigration and other issues. The last US government shutdown was in 2013.

This time around, Democrats want any short-term spending legislation to include protections for young undocumented immigrants known as "Dreamers".

Republicans in turn say they will not negotiate on immigration until Democrats gave them the votes needed to reopen the government.

Many federal workers stayed home but federal government operations varied from agency to agency, with a number of critical functions continuing. The shutdown will not interrupt combat operations in Afghanistan and other military activities, the Defence Department said, and federal law enforcement officers remained on duty.

The 17 Washington area museums in the Smithsonian network are open despite the shutdown, although their plans are unclear for Tuesday. The National Zoo, which is part of the Smithsonian, also remained open on Monday.

A group of bipartisan senators meeting at the Capitol said they made progress but some senators wanted a firmer commitment from Senate Majority Leader Mitch McConnell, a Republican, on protecting "Dreamers" and on other issues.

"So some Democrats have to convince Mitch McConnell: stronger language results in an outcome," said Republican Senator Lindsey Graham.

As the meeting broke up, McConnell told the Senate he hoped bipartisan agreement could be reached on issues such as military spending, immigration and border security before February 8.

If not, he reiterated a pledge to take up legislation that would address the fate of illegal immigrants brought to the US as children, border security and related issues - if the government remains open.

"We need to move forward. And the first step, the very first step, is ending the shutdown," he said.

The Senate recessed before the scheduled vote and Democratic leaders huddled with their members, some of whom sounded pleased with McConnell's words.