Sen. John McCain, R-Arizona, was the sole Republican who opposed Mulvaney's nomination because of his advocacy for budget cuts to the military.
Mulvaney's confirmation promises to accelerate work on Trump's upcoming budget plan.
Senate majority leader Mitch McConnell criticized Democrats for "unnecessary delay" upon Mulvaney's approval.
Mulvaney's poor record on national-security issues is at odds with Trump's promise to rebuilt the USA military, said McCain, the influential chairman of the Senate Armed Services Committee.
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The Senate on Wednesday voted 52-48 along party lines to advance Mulvaney to a final, up-or-down vote Thursday.
"I believe Mick Mulvaney was brought in to provide a different perspective and based on my conversations with Mick, he thinks that the White House will welcome that different perspective", U.S. Rep. Justin Amash, R-Mich., a friend of Mulvaney's, told reporters at a Wednesday panel discussion of House conservatives.
"The House's loss is President Trump's gain", the North Carolina Republican said in a statement. Mike Enzi, chairman of the Budget Committee. McCain, chairman of the Senate Committee on Armed Services, agrees.
Giving Mulvaney authority to write the president's budget and advise the administration on fiscal policy would continue six years of "Washington dysfunction", which has "imposed very real consequences on the thousands of Americans serving in uniform", McCain said. "He authorized and supported amendments to cut national defense funding year after year after year". He was one of multiple Cabinet nominations that the minority party had targeted for special scrutiny in the confirmation process for President Donald Trump's executive nominees. This is not personal.