Senator Susan Collins, Republican of Maine and the chairwoman of the Senate Appropriations Committee, said she worried about the implications for global health, particularly because some of the funding that the president targeted has “saved more than 26 million lives.”

Lawmakers from both parties later echoed some of those criticisms, prompting Ms. Collins to conclude the hearing by saying that it showed the “depth of concerns about this rescission from members on both sides of the aisle” with the White House’s plans. A spokesperson for the senator later confirmed that she was drafting an amendment to change the package when it reached the Senate floor.

Democrats took more direct aim at Mr. Vought, in a series of combative exchanges that challenged not only the proposed cuts but also the president’s broader views about his own spending powers.

At one point, Senator Patty Murray of Washington, the top Democrat on the panel, pressed Mr. Vought to say whether the White House would try to strike federal funds even if Congress did not approve, an idea that the budget chief has raised publicly in recent days.

Mr. Vought declined to rule out that possibility and defended his tactics and legal reasoning. He stressed repeatedly that there were other ways for Mr. Trump to cut spending, in comments that suggested the White House could try to sidestep a vote in Congress.