Sen. Lindsey Graham, who is among a bipartisan group of senators attempting to find a compromise and end the shutdown, pointed the finger at Stephen Miller, a senior policy adviser.
"The great deal-making president sat on the sidelines", Schumer said.
House of Representatives Republicans have been told by their leaders to plan on voting on a measure to re-open the government immediately.
The vote to end the filibuster was 81-18, clearing the way for passage of the stopgap spending bill.
Schumer told Senate Majority Leader Mitch McConnell that he expected Republicans to make good on a pledge to address Democrat concerns over the Deferred Action on Child Arrivals (DACA) program that shields immigrants brought to the country as children from deportation, but expires on March 5.
Democrats also objected: "That would be the end of the Senate as it was originally devised and created going back to our Founding Fathers. We have to acknowledge a respect for the minority", Sen. Dick Durbin, D-Ill., on ABC's "This Week" today.
"Unfortunately, we can not answer your call today because congressional Democrats are holding government funding - including funding for our troops, and other national security priorities hostage to an unrelated immigration debate", the voice message says.
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. Republican Sen. John McCain of Arizona was in getting treatment for brain cancer.
"After several discussions, offers and counteroffers, the Republican leader and I have come to an arrangement".
Democrats have sought to use the spending bill to win concessions, including protections for roughly 700,000 younger immigrants.
Luna received Deferred Action for Childhood Arrivals or DACA in 2012 as part of an Obama administration executive order which gave almost 800,000 undocumented immigrants the chance to go to college and work in the U.S, but still provided no path to citizenship. While there have been multiple bills introduced in Congress, GOP leadership has not committed to bringing up any specific legislation. Democrats blocked the spending bill last Friday, demanding a commitment on DACA beneficiaries who include an estimated 8,000 Indians. Republicans argued that Democrats shuttered the government over "illegal immigration" in a bid to gin up enthusiasm among their base. "We believe that you need to start in the House and it has been my position consistently, you start in the House with the most conservative bill, you send it to the Senate, it gets moderated in the Senate, and then comes back". It remains to be seen whether Democrats will insist on a more concrete deal before shifting their stance, with (Democrat) Senate Minority Leader, Chuck Schumer, blaming the shutdown squarely on the President: "Americans know why the dysfunction is occurring - a dysfunctional president".
In exchange for a $20 billion commitment for a wall along the southern border, Schumer said Democrats were seeking a commitment to vote on one large spending bill that included a path to legalization for the DREAMers, disaster aid and other domestic spending.
But sources with knowledge of the discussions said a wall alone does not come close to meeting White House demands. On Saturday, White House aides said they would not negotiate on immigration until the government re-opened.
Sen. Joe Manchin, D-W.V., said Collins' office became "our little Switzerland", where lawmakers could talk with each other "and not at each other".
A key reason why the White House has not agreed to a deal that would reopen the federal government is that West Wing officials are insisting on almost all of their demands for clamping down on the nation's immigration system, sources inside the White House and Capitol Hill said.
Throughout the day there were few outward signs of progress, as lawmakers took turns delivering animated speeches to near empty chambers to explain why the other party is to blame.
The White House put out a brief statement Sunday detailing the president's activities, saying the administration was hard at work.