The hearing for Ronny Jackson, Trump's White House doctor and a Navy rear admiral, was scheduled for Wednesday.
"Some Republican colleagues have told me that they think the hearing should be postponed, which certainly deserves consideration," said Sen. Richard Blumenthal, D-Conn., a member of the Senate Veterans Affairs Committee.
"I think there may well be a need for more time, in fairness to Admiral Jackson, so he and the administration have an opportunity to answer these questions fully and fairly," he said.
Blumenthal declined to discuss why more time might be needed.
White House and VA officials were also discussing a delay with key allies outside the administration
A spokeswoman for Sen. Johnny Isakson, R-Ga., the committee's chairman, did not return requests for comment.
Trump selected Jackson to head the VA last month after firing former Obama administration official David Shulkin following an ethics scandal and mounting rebellion within the agency. But Jackson has since faced numerous questions from Republican and Democratic lawmakers as well as veterans groups about whether he has the experience to manage the massive department of 360,000 employees serving 9 million veterans.
Sen. Mike Rounds, R-S.D., and a committee member, said Jackson's small staff at the White House will be an issue as he prepares to lead the VA.
"We've got 360,000 people there," he said. "Are they going to manage the secretary or is the secretary going to manage the VA? That's a good question to ask, and he needs to answer it. He needs to be the leader. A lot of folks want to be led and managed."
Rounds said the committee still needs more paperwork from the White House on Jackson before the nomination can go forward.
AP Congressional Correspondent Lisa Mascaro and Associated Press writer Matthew Daly contributed to this report.
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