He called for "changing the rules", or for more Republicans to be elected to the upper chamber in 2018.
Republicans negotiated the massive budget deal, leaving out funding for some of Trump's major priorities, like the border wall, but agreeing to spending many GOP supporters say they find problematic, like entitlement spending that fully funds Planned Parenthood.
Republicans hold 52 of the Senate's 100 seats.
Meanwhile, Senate Majority Leader Mitch McConnell said Tuesday that nearly no senators would support removing the legislative filibuster, which is the procedural tool that can be overcome only by a so-called supermajority of 60 votes.
Mulvaney said Democrats triggered Trump by taking a victory lap over the recently reached bipartisan spending deal just agreed to that funds the government through September, avoiding a government shutdown now.
In spite of the budget outcome and his call for a government shutdown in five months, Trump later publicly praised the funding plan.
Congress is expected to vote this week on the $1.1 trillion spending bill.
"They're walking around trying to make it look like they pulled one over fast on the President". "I think it is silly".
Mulvaney condemned Democrats - who argue that they won numerous battles within the bill - for celebrating the spending deal as a victory for their party.
Sean Spicer: Trump will not announce Paris climate decision until after G7
Officials from Barack Obama´s administration argue that the deal is good for the United States. The Paris agreement will be discussed at an upcoming summit in Taormina, Italy on May 26-27.
His comment frustrated some of his fellow Republicans in Congress, who chafed at the suggestion that the White House could dictate Senate rules, or send a message that a shutdown, which costs the economy millions, was desirable.
Republicans were scrambling yesterday to put together enough votes to pass Obamacare replacement legislation. The truth of the matter though is now we've averted a government shutdown in a way that allows the president to fund his priorities, " Mulvaney said.
Roy Blunt, a leading Republican appropriator, said he understands Trump's frustration, but says Trump's Republican Party has often been in the minority and realized a filibuster can help force compromise, and that the founders designed a government that makes change hard.
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.
Democratic Senator Patrick Leahy called Trump's threat "a sour and shameful note to kick off negotiations" for next year's spending plan, pointing to billions of dollars of losses triggered by the shutdown four years ago.
Trump initially asked Congress for a $1 billion down payment to build 62 miles of the border wall.
Mr. Mulvaney said he didn't anticipate a government shutdown in September, but he understood the president's frustration over Democrats "spiking the ball" after negotiating with them in good faith, and that a shutdown could happen if they didn't "behave any better".
He correctly noted that the pending measure would be a victory for Republicans because the administration succeeded in breaking the link - forged over several Obama-era spending deals - that required that any increases in military spending be matched by an equal, dollar-for-dollar increase for nondefense programs.
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