Mulvaney said the White House will turn next to the 2018 budget, and wouldn't balk at a government shutdown if necessary to get it passed, echoing Trump's tweet earlier in the day that the United States "needs a good shutdown".
The Senate requires 60 votes to end debate for nearly any bill and Republicans only have a 52-48 edge.
"It's time for Speaker Ryan and the Republican Party to stage an intervention", House Minority Leader Nancy Pelosi said, as reported by CQ Rollcall's Kellie Mejdrich.
Democrats could have held up any deal in the Senate with a filibuster, since Republicans only have a 52-seat majority and would need 60 votes to move legislation forward.
The compromise reached by Republicans and Democrats calls for an increase in military spending, which has been one of Trump's priorities.
In a series of tweets on Twitter, Trump lashed out demanding a future government shutdown and calling for the Senate to eliminate the legislative filibuster.
US President Donald Trump says the nation "needs a good shutdown in September" to fix a "mess" in the Senate. The lowered threshold does not apply to legislation and Senate Majority Leader Mitch McConnell, along with 60 senators, have said they would oppose applying the option outside of judicial nominees.
"We all worked as a team", Schumer said. Mulvaney instead trumpeted the increases in defense spending and money for border security - despite the lack of "brick and mortar" allocations for the wall - as well as wins for proponents of school choice. Typically, a Republican president with a Republican-controlled House and Senate wields considerable leverage.
Trump's hint towards starting a government shutdown was not clear, as the president has been known in the past to take such stances on important issues before ultimately standing down.
"I don't think there is any Democrat who wanted a shutdown", Sen.
Trump also had to give up on some requests of funding cuts for medical research and community development programmes.
"All right", Mulvaney told reporters at one point. Asked to explain Trump's advocacy for a shutdown, Mulvaney said, "Right now I'm not anxious about September, I'm anxious about this deal that's in front of us".
"What you heard the president express this morning was frustration over how he was treated as part of the negotiations", Mulvaney said during a press briefing at the White House on Tuesday.
"I don't think there's any Democrat who wanted a shutdown", Coons said on CNN, according to the Washington Examiner. "And we're hopeful that we can see as we go through the 2018 process is more of a Republican-driven process, especially in the House, which would be a little bit more typical".