Mr Mulvaney told federal agencies they should execute their contingency plans and instructed federal employees to report to work on Friday to "undertake orderly shutdown activities".
The deal, if approved, would also fund the federal government until March 23, averting a second shutdown this year and giving lawmakers six weeks to resolve their differences over immigration policy and find agreement on a full-year budget.
The House passed the bill Thursday along partisan lines after hours of debate during which Democrats decried the measure as another way of diverting money from the state's public schools.
Two hours after the setback, congressional leaders scrambled to end the standoff in the middle of the night.
"This really is the moment where it has become clear that despite record levels of debt and approaching trillion dollar deficits, Congress has stopped caring about what they're doing to the fiscal health of the country", said Maya MacGuineas, head of the Committee for a Responsible Federal Budget, a group that advocates for long-term fixes to Washington's debt problems.
"I know there is a real commitment to solving the DACA challenge in both political parties", Ryan said during his weekly press conference on Thursday on Capitol Hill.
Durbin said he still expects a neutral bill.
But Pelosi said on the House floor that because House Speaker Paul Ryan has yet to promise an immigration vote, the emerging budget pact "does not have my support, nor does it have the support of a large number of members of our caucus".
The sheer mechanics of moving the proposal through the USA legislative branch require many congressional leaders as well as rank-and-file members to work in close coordination in order to beat that deadline. Pelosi said she would vote against the bill unless Ryan gave assurances that he would allow an open debate on immigration legislation.
The White House has not wavered from the four pillars, arguing that such reforms would prevent another Dreamers crisis in the future.
"I was getting whipped every which way at this point", he said. "We will bring a solution to the floor, one the president will sign".More news: East Ghouta 'drowning in blood' after third day of bombing
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Rep. Kurt Shcrader, D-Ore., said "do what you want to do" was the message from Pelosi.
"My experience with Paul Ryan is I don't agree with him, I think he has challenges in his own caucus, I wouldn't call him the strongest speaker in my memory, but he is an honorable man", he said.
"I think we got a way forward that seems to be fair to everybody", Graham said.
Enough Democrats -73 of them - voted "yes" to offset the 67 Republican defections on the bill to get it over the finish line.
Faso refused to comment on the whole spending package until the Senate voted on a final version, but he highlighted one aspect of the bill he called a win for upstate NY.
The bill includes massive spending increases for the military that Republicans wanted along with a big boost in domestic spending demanded by Democrats.
In the 2013 budget agreement, the only other time the caps got raised, spending increased $63 billion over two years under the parity rule, but the bill also cut spending further down the road to pay for it.
Exiting the Senate chamber at 2 a.m. Friday morning, Republican Sen. Kevin McCarthyKevin Owen McCarthyDems confront Kelly after he calls some immigrants "lazy" McConnell: "Whoever gets to 60 wins" on immigration Hoyer: DACA deal a long ways off MORE (R-Calif.) and Steny HoyerSteny Hamilton HoyerDems confront Kelly after he calls some immigrants "lazy" McConnell: "Whoever gets to 60 wins" on immigration Hoyer: DACA deal a long ways off MORE (D-Md.) - has failed to get a broad agreement favored by the White House.
The partial shutdown began just after midnight, when the government, operating on the latest in a series of short-term spending bills, ran out of money because Congress missed its deadline to pass a new one.
Republican and Democratic leaders in the Senate are nearing agreement on a two-year budget bill to avoid another government shutdown, Senate Democratic Leader Charles Schumer said Tuesday. That additional spending worries some deficit-minded Republicans, and some Democrats are unhappy that immigration isn't part of the measure.