The White House rejected Schumer's criticism.
But the White House appeared in no mood for bipartisanship or magnanimity after a shutdown that overshadowed Trump's first anniversary in office.
Democratic support for any spending bill is essential with Republicans holding a razor-thin 51-seat majority in the 100-member Senate.
There have been four government shutdowns since 1990.
McConnell has long defended the filibuster.
Republicans are pinning the blame squarely on the Senate Democrats.
"He's gotten more done in one year than arguably any president in history", Eric Trump said, on Justice with Judge Jeanine. But he also said, "The question is, when do you use it".
Trump has made repeated calls this year to end that rule, and did it again Sunday in a tweet. "Or do they want to retain that issue and run, and say [that] Democrats wouldn't let us build this wall?"
Schumer complained later that dealing with the president was like "negotiating with jello".
President Donald Trump has done little publicly, aside from tweeting, during the shutdown. Once Mr. Trump signs it, the government will reopen.
But Trump said the "nuclear option" of a simple-majority vote was necessary.
Sanders maintains that government funding legislation must provide legal status for the roughly 700,000 young immigrants brought illegally to the U.S.as children.
The White House has said it won't negotiate on immigration until Democrats vote to reopen the government.
Pence told USA soldiers stationed near the Syrian border on Sunday: "You deserve better". Miller has been among the leaders in the White House who has guided the president to push for ending chain migration and curb the diversity visa lottery program. The shutdown will not interrupt combat operations in Afghanistan and other military activities, the Defense Department said, and federal law enforcement officers remained on duty.
During the 8 1/2-hour Sunday session, Senate Democrats tried a number of times to offer very short-term continuing resolutions in order to force both sides to negotiate more intensively. Sen.
The senator from Kentucky said Sunday on CNN's "State of the Union": "It's gamesmanship and it's partisanship".
Democrats condemned the ad, and Republican House Speaker Paul Ryan told "Face the Nation", "I don't know if that's necessarily productive".
"It is abundantly clear that the Senate can not make progress on any of these crucial matters until the government is re-opened", McConnell said on the Senate floor, as he promised to allow an immigration policy process so long as the government was not shut down. The measure gained 50 votes to proceed to 49 against, but 60 were needed to break a Democratic filibuster. The Senate adjourned without voting today, guaranteeing the shutdown would continue into a third day.
The Republican president is floating the idea of doing away with the 60-vote threshold to advance legislation and deny the minority party the chance to stall.
Durbin tells ABC's "This Week" that "we have to acknowledge a respect for the minority". In the last one, more than 800,000 government workers were put on temporary leave.
Her agency is expected to keep providing what it calls "minimal support" during the shutdown and has said it will keep responding to influenza outbreaks. He says, "This is pure politics".
Mulvaney was a conservative member of the House in 2013 when a showdown over "Obamacare" funding led to the last shutdown.
That threat prompted a bipartisan group of Senate moderates to huddle for a second day today in hopes of crafting a plan to reopen the government.
Both parties blamed each other throughout the weekend for the impasse.
Speaking to USA troops at a military base in the Middle East, Vice President Mike Pence said, "We're not going to reopen negotiations on illegal immigration until they reopen the government and give you, our soldiers and your families, the benefits and wages you've earned".