WASHINGTON — President Donald Trump suggested Tuesday that his pick for Veterans Affairs secretary might want to withdraw after the emergence of allegations about inappropriate workplace behavior, including over-prescribing prescription drugs and drinking on the job.

Trump said he would stand behind Dr. Ronny Jackson, calling the White House doctor “one of the finest people that I have met.” But he questioned why Jackson would want to put up with the scrutiny, which he characterized as unfair.

“I wouldn’t do it,” Trump said. “What does he need it for? What do you need this for? To be abused by a bunch of politicians that aren’t thinking nicely about our country?”

He said Jackson would make a decision soon.

Trump spoke at a White House news conference with French President Emmanuel Macron shortly after the Senate Veterans Affairs Committee announced that Jackson’s confirmation hearing, scheduled for Wednesday, would be postponed indefinitely while senators looked into the allegations.

“We take very seriously our constitutional duty to thoroughly and carefully vet each nominee sent to the Senate for confirmation,” said the chairman, Sen. Johnny Isakson, R-Ga., and the top Democrat on the committee, Sen. Jon Tester of Montana. “We will continue looking into these serious allegations and have requested additional information from the White House to enable the committee to conduct a full review.”

Asked if Jackson’s nomination is still viable, Isakson responded, “We’ll see.”

The two lawmakers sent a letter to Trump on Tuesday requesting additional information about Jackson, who has served as a White House physician since 2006. It demands any communication between the Pentagon and the White House for the last 12 years regarding “allegations or incidents” involving him.

With Congress set to recess Friday for a week, Tester said the earliest a hearing could be held would be in about 10 days but it was too soon to tell. “We’re vetting hard right now,” he told reporters. “We still have more information to find out.”

Allegations began surfacing late last week involving Jackson’s workplace practices, including claims of inappropriate behavior and over-prescribing prescription drugs, according to two aides granted anonymity to discuss the situation. The complaints the White House heard include that he oversaw a poor work environment and that he had drunk alcohol on the job, according to an administration official who demanded anonymity to speak on a sensitive personnel matter.

Isakson told fellow GOP senators over the weekend about the allegations, prompting those on the panel to support delaying the hearing.

“These concerns are bipartisan,” said Sen. Richard Blumenthal, D-Conn., and a member of the committee. “The viability of his nomination depends on the administration’s ability to provide answers quickly, thoroughly, accurately and honestly.”

Democrats on the committee assembled privately late Monday. Tester reiterated to the other senators that the allegations were out there, one aide said. But no specific evidence of wrongdoing was offered.

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 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.

A doomed nomination would be a political blow to the White House, which has faced criticism for sloppy vetting of Cabinet nominees and tough confirmation battles in a Senate where Republicans hold a slim 51-49 majority. Prior to Jackson’s nomination, Trump had told aides and outside advisers that he was fond of Jackson personally and was said to be particularly impressed with Jackson’s performance at the White House press room podium in January, when he offered a glowing report on the president’s physical and mental well-being.

Senate Minority Leader Chuck Schumer, D-N.Y., said the American people were the losers in a shaky nomination effort. The Trump Cabinet, he said, “is turning into a sad game of musical chairs.”

Sen. Susan Collins, R-Maine, who is not on the veterans panel, noted that the allegations against Jackson arose after Trump nominated him. “I don’t know whether this is an aberration or not, but it certainly is something that bears looking into.” She said recent allegations of ethical violations in Oklahoma by EPA Administrator Scott Pruitt also raise questions about White House vetting.

Sen. Patty Murray, D-Wash., a member of the Senate veterans committee, said Trump “either didn’t care or didn’t bother to send a fully qualified VA nominee.”

Late Monday, Jackson was still pursuing support. He held a late-afternoon conference call with veterans groups from West Virginia and the state’s Democratic Sen. Joe Manchin, a member of the committee, whose vote could be vital for support.

Sen. Mike Rounds, R-S.D., a member of the committee, said Jackson’s small staff at the White House will be an issue as he is considered 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.”

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