The current government funding expired on Friday midnight as the Senate failed to advance a stopgap spending bill, which had passed the House of Representatives and would fund the government through February 16.
It will now go to the House of Representatives.
But if there is a Senate compromise that includes immigration provisions, the House speaker will have to sell it to a Republican caucus that has drawn a hard-line on the immigration issue.
President Donald Trump kept a low profile Sunday, and has been accused by Democrats of shifting his positions on a DACA deal, reportedly scuppering a last minute agreement under the influence of hard-right adviser Stephen Miller.
There is growing optimism that the Senate will be able to muster the votes necessary to advance a three-week funding measure to reopen the federal government, Republican and Democratic aides and lawmakers say.
But Schumer said on the Senate floor it was time to get back to work, and lashed out at Trump.
McConnell's promise to address DACA in February might not be much, but it may be just enough to win the Democratic support needed to end the shutdown. "As a result, there is now a path forward to help the Dreamers, fund the military and other agencies and provide Florida with the hurricane disaster assistance it still needs".
Trump kicked off Monday morning by accusing Democrats of playing to the "far left base". The measure also extended a federal children's health insurance program.
Schumer said the 60-hour shutdown could have been avoided if US President Donald Trump had been prepared to compromise.
The US Senate votes today on a bill to temporarily restore federal funding and end a three-day shutdown that has delayed federal services and forced hundreds of thousands of civil servants to take unpaid leave.
"I am happy to continue my discussion with the majority leader about reopening the government", Schumer said. "They don't want to do it but are powerless!" he tweeted.
"Please stop", Ms. Collins said quietly to colleagues on the floor as Mr. Schumer harangued Mr. Trump and Mr. McConnell.
McConnell dismissed the suggestion, noting that the rule will be welcomed once the Republicans become the minority in the Senate.
Senate rules impose a threshold of 60 votes to break a filibuster, and Senate Republicans now hold a slim majority of 51 votes, meaning even if they can unite their members, they need nine more votes to end debate.
The last government shutdown, in October 2013, lasted for 16 days and about 850,000 federal employees were furloughed.
"If we've learned anything during this process, it's that a strategy to shut down the government over the issue of illegal immigration is something the American people didn't understand and would not have understood in the future", Senate Majority Leader Mitch McConnell (R-KY) said shortly before the vote.
Democrats refused to vote for the bill unless they secured protections for recipients of the Obama-era programme.