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"I'm responsible for getting the money together to build the wall, and that's what I'm doing," he said on ABC News' "Good Morning America."
Trump's push for a border wall between the United States and Mexico was the cornerstone of his 2016 presidential campaign, and he insisted that Mexico would pay for it. Mexico's President Enrique Pena Nieto has said his country will not do so.
Mulvaney, who unveiled Trump's budget blueprint Wednesday, said the proposed cuts and spending reflect Trump's campaign promises.
"The president wrote a budget for the nation, and we wrote a budget based upon his campaign promises, and that's what you see in the budget," Mulvaney said. "We took his words and turned them into numbers. The president promised a wall. He's going to deliver it."
In the budget blueprint, Trump's promised border wall will get $1.5 billion, with possibly more funds flowing to the project in next year's budget. The money will provide for a couple of "pilot cases" to see what kind of wall structure is most cost efficient and effective, Mulvaney told reporters Wednesday.
He said on "GMA" this morning that the money the president seeks to start the wall is "not that much money in a trillion-dollar discretionary budget."
While a balanced budget is not achievable this year, Mulvaney said, the budget blueprint doesn't add to the deficit. He added that the Trump administration will release its full federal budget in May.
"This is a budget blueprint. It's really the spending part of the budget," Mulvaney said. "This is the first piece of the budget to allow the spending process to start in Congress."