Updated at 3:53 p.m. ETPresident Trump cast doubt on whether embattled Rear Adm. Ronny Jackson should remain the nominee for secretary of veterans affairs but said the decision was up to Jackson."It's his decision," Trump said Tuesday during a bilateral news conference with French President Emmanuel Macron.Trump said that if he were Jackson, "I wouldn't do it. I wouldn't do it. What does he need it for? To be abused by a bunch of politicians that aren't thinking nicely about our country? I really don't think personally he should do it but it's totally his — I would stand behind him — totally his decision."The comments come as Jackson's nomination appears in jeopardy amid "serious allegations" about his workplace behavior, according to several senators and aides.The allegations are so far unsubstantiated, but they prompted the Senate Veterans Affairs Committee to postpone a hearing on the nomination pending further investigation. Trump called Jackson "one of the finest people that I have met." (In fact, at one point, Trump remarked that "actually in many ways I'd love to be him.") He said multiple times that he asked Jackson on Tuesday, "What do you need this for?"But Trump left the next move up to Jackson. "It's totally his decision," the president said, blaming Democratic obstruction and scrutiny.Jackson showed no indication of withdrawing Tuesday. He was on Capitol Hill, making the rounds with key senators on the committee. Reporters caught up with him on his way to Sen. Jerry Moran's, R-Kan., office."I was looking forward to the hearing tomorrow," Jackson said, per video captured by MSNBC. "Kind of disappointed that it's been postponed, but I'm looking forward to getting it rescheduled and answering everybody's questions."Asked if he "categorically denied" the allegations against him, he said, "I'm looking forward to the hearings, so we can sit down, and I can explain everything to everyone and answer all the senators' questions."Veterans Affairs Committee Chairman Johnny Isakson, R-Ga., and the top Democrat on the committee, Sen. Jon Tester, D-Mont., sent a letter to Trump on Tuesday requesting additional documentation related to Jackson's tenure as the president's doctor and his role leading the White House medical team. "We take very seriously our constitutional duty to thoroughly and carefully vet each nominee sent to the Senate for confirmation," the pair wrote. "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."The letter requested information about rumored Pentagon inspector general reports said to detail allegations into Jackson's conduct. When asked Tuesday whether he had any such reports, Tester said he did not. Tester said Jackson's nomination remained "absolutely" viable. "I think we still have more information we need to find out."Jackson himself, though, said categorically in the MSNBC video that there was no inspector-general report about the allegations. "No, there was not," he said before brushing off questions about whether he would withdraw. Senate Veterans Affairs Committee member Mike Rounds, R-S.D., told NPR's Morning Edition that Jackson is accused of "serious" but "unsubstantiated allegations." "We have been given a brief sketch of what they are, but I'd prefer not to discuss them at this time," Rounds told NPR.Rounds added: "These are serious allegations, and they are ones we'd certainly want to get through."The allegations began circulating among staffers on Capitol Hill late last week, but so far, no details have been directly confirmed and lawmakers have declined to be specific. According to two senators on the committee, several people, including military personnel, approached the Senate Veterans Affairs Committee beginning late last week with allegations against Ronny Jackson of inappropriate behavior in the workplace."The allegations have come from people that are in the military, or used to be in the military, former military people who came forward. Some I assume approached committee members, others engaged or gave other names that committee staff could call. All of them were willing to talk," said Sen. Sherrod Brown, D-Ohio, who said he had not spoken to anyone directly who came forward, but that committee staff has and that those conversations began last week. Brown characterized those speaking to the committee as "people that work with him, many that like him. It's not a question of liking him; it's a question of what he's done in the past that would have an impact on this job."He declined to comment on the substance of the allegations. "None of it's confirmed. I will recite none of what I heard. I will say it's clear the president's people didn't make very many of these calls."Sen. Richard Blumenthal, D-Conn., likewise said that the allegations were brought to the committee's attention but that none of the accounts had been corroborated. The committee has not received any supplemental or verifying documents, like inspector general reports."I'm not going to talk about who the people were or their credibility. The credibility of the questions need to be tested against the facts," he said. "There were complaints to the committee. I'm not going to talk about the specific sources or the specific allegations. We need facts.""Vetting failures unfortunately are symptomatic of a broader failure [of the Trump administration] to properly review and scrutinize the records of its nominees," Blumenthal said. "The viability of his nomination depends on the administration's ability to provide answers to questions quickly, thoroughly, accurately and honestly."Jackson currently serves as White House physician. He defused doubts about the health and fitness of Trump in January, describing the president's medical condition in emphatically glowing terms. Jackson is a former combat surgeon who served with Navy bomb disposal units and instructed underwater salvage teams.The White House defended Jackson Tuesday."Admiral Jackson has been on the front lines of deadly combat and saved the lives of many others in service to this country," said Hogan Gidley, deputy White House press secretary. "He's served as the physician to three Presidents— Republican and Democrat — and been praised by them all. Admiral Jackson's record of strong, decisive leadership is exactly what's needed at the VA to ensure our veterans receive the benefits they deserve."Trump picked Jackson to succeed David Shulkin, who was forced to resign as VA secretary after an inspector general's report uncovered inappropriate expenses.The allegations about Jackson add to worries from senators in both parties that Jackson is not qualified to run the veterans agency. Several senators have questioned whether Jackson has the managerial experience to lead a department with 360,000 employees, responsible for the care of some 9 million veterans.Virginia Democrat Tim Kaine told reporters Monday that the veterans agency needs a strong manager to help the agency rebound from years of scandal and mismanagement. "As a physician, I don't think people have questions," Kaine said. "But knowing the size and scope of the challenges in the VA and the size of the operation and what we need to do, I think there's a lot of skepticism."Jackson currently oversees a staff of several dozen in the White House Medical Unit. While Jackson is primarily responsible for the president's health care, he also offers treatment to White House staffers and occasionally journalists — something he reminded reporters during a January briefing."If something should happen to you over the next few months and you should fall ill at some point, most likely I will be the one called to come take care of you," he said. "So when you ask your questions, please keep that in mind."Jackson is also a blank slate on one of the major policy questions facing the VA: how large a role the private sector should play in veterans' health care. Major veterans service organizations are concerned he might oversee a push toward privatization.In a floor speech Tuesday morning, Senate Minority Leader Chuck Schumer, said Jackson's troubled nomination was indicative of larger issues facing Trump administration nominees. "So, the president is putting forward nominees without appropriate vetting, and it's our job to vet, and we will not be rushed through, particularly when this administration has such a poor record of looking at the qualifications and the problems that each nominee brings," said Schumer. News of the postponement came a day after nomination of CIA Director Mike Pompeo, another Trump pick who had appeared in peril, cleared a key Senate committee on the path to becoming the next secretary of state.NPR's Scott Horsley and Domenico Montanaro contributed reporting to this story. Copyright 2018 NPR. To see more, visit https://www.npr.org/.