Hours after a marathon session Friday failed to produce agreement on a stopgap measure to fund federal operations through February 16, Senate Majority Leader Mitch McConnell urged his colleagues to "end the foolishness" and pass a temporary spending bill.
Mr Trump accused the Democrats of being "far more concerned with illegal immigrants than they are with our great military or safety at our unsafe southern border".
"Democrats are holding our Military hostage over their desire to have unchecked illegal immigration. If stalemate continues, Republicans should go to 51 per cent (Nuclear Option) and vote on real, long term budget", Mr Trump tweeted on Sunday. "It's their job to keep the government open", Schumer said.
The White House traded salvos with Senate Democrats Saturday as both sides dug into opposing positions as the first day of the federal government shutdown dragged on.
President Trump was largely quiet on the issue over the weekend, though he suggested in a tweet on Sunday morning that Republicans should change Senate rules to allow the bill by a simple majority.
"Most Democrats refuse to support the bill because it does not do anything to protect the "Dreamers" - 800,000 people brought to the USA illegally as children, who face deportation after Mr Trump cancelled a programme to shield them", reports the Financial Times.
Senate Republicans, however, have said that's not a solution they're taking seriously.
She also told Al Jazeera that "the president is feeling a bit of frustration because if you recall in 2013, he roundly criticised President [Barack] Obama for not having the skills and the leadership to strike a deal to bring people together".
But Democrats said it was Republicans who were at fault.
"If he does not, of course, and I expect he will, he will have breached the trust of not only the Democratic senators, but members of his own party as well", Schumer said.
Lawmakers are at odds over a range of defense spending and immigration issues, including a legislative fix for almost 800,000 undocumented young people brought to the U.S.as children. The House of Representatives also passed the spending bill today, and now, it moves on to Trump's desk.