And they'll get a bit of help from an Obama-era law to do it.
Democrats have already made their opposition plain: "President Trump has shown that he does not value the future of our children and working families," Rep. Nancy Pelosi (D-Calif.), the minority leader in the House, said Thursday. The budget, she said, "fails to recognize that the health of America, the strength of America, does not just depend on our military."
Ordinarily, Pelosi and her Democratic colleagues would have little say over the federal budget. Republicans control both the House and the Senate, and Congress typically begins putting together the government's budget through a process known as reconciliation, which prevents the party in the minority from throwing up a filibuster in the Senate.
There's where the past will come back to bite Trump's effort: In 2011, Congress and former President Obama enacted a strict set of federal spending limits -- the "sequester," as it is called.
As part of the deal, which put limits on both military and domestic spending, any proposal going beyond those caps must overcome a potential filibuster in the Senate.
Trump's budget, and its $54 billion in new defense spending, meets that criterion. "The president has said he’s going to undo the military sequester," Trump's budget chief, Mick Mulvaney, told reporters on a conference call Wednesday. "This budget does that."
With 46 seats, not counting the two independent senators who typically join their caucus, Democrats have more than enough to mount a filibuster. Trump would need their cooperation to enact the budget.
Yet Trump is unlikely to find Democratic senators who would support his budget, which would eviscerate public agencies outside of the military.
Trump's proposal would provide more funds for the Pentagon, for public charter schools and for building a wall along the border with Mexico. The president would gut environmental protection and drastically reduce funding for scientific research across the government. Less money would be available to help poor mothers buy food for their families and to help impoverished households heat their homes.
Some Republicans might be opposed as well. Trump's budget does not reduce federal spending, instead shifting expenditures from other agencies to the Pentagon. Libertarians such as Sen. Rand Paul (R-Ky.) and ideologically moderate, fiscally conservative lawmakers such Sen. Rob Portman (R-Ohio) have argued the government should spend less and borrow less money.
The legislative branch, not the president, is responsible for the government's budget. Trump will not be able to make his budget reality without more support from lawmakers.
Apart from the sequester, there is another reason Republicans might not be able to enact Trump's budget this year: Repealing Obamacare could take months.
Republicans are relying on reconciliation to repeal Obamacare without confronting a Democratic filibuster in the Senate. To use reconciliation to instead begin work on a budget, Republican lawmakers would have to start over, scrapping the progress they have made so far on dismantling Obamacare.
Some Republican lawmakers, however, have objected to the legislation that their party has advanced to repeal Obama's reform, and many observers expect the GOP debate over health care to continue through the summer. By then, the start of the federal government's fiscal year for budgeting purposes in October will be approaching, leaving lawmakers little time to put a new budget in place.
"We're very late here," said William Hoagland, who worked in Congress for decades as an aide to senior Republican lawmakers. "That just doesn’t give them a lot of time to go through the process."
Hoagland said it was "terribly unrealistic" to think that Congress would act on Trump's budget.
"This is Bill Hoagland speaking, and I can only say: No, it’s not realistic," he said.
What is more likely, Hoagland predicted, is that Congress will keep things simple by maintaining the current levels of funding for federal agencies, passing what is known as a continuing resolution.
That does not mean that Trump's budget is irrelevant, however. For the first time, the president has had to show how he would deliver on some of the promises he made during the campaign, noted Bill Gale, who served as an economist in President George H.W. Bush's White House.
"The president’s budget proposal matters because it’s a statement of the administration’s priorities and goals," Gale said. "People can look at those numbers and look at their implications and understand more specifically what he is proposing."
For instance, in order to dedicate funds to the wall along the border and to augment the Pentagon's budget, Trump proposes compromising on his other goals. He would make less money available for some infrastructure projects and limit counterterrorism grants for local law enforcement.
The budget, Gale said, "doesn't allow people to hide behind the rhetoric."