President Trump said he hasn't heard about the allegations against Ronny Jackson, his Veterans Affairs secretary nominee, but he said several times during a news conference Tuesday that he told Jackson, "What do you need this for?" The president accused Democrats of obstructionism and said he didn't want to put a man through "this process," calling it "too ugly and too disgusting."

Mr. Trump said that he "would definitely stand behind him," and he called him "an extraordinary person" and "a great doctor." While the president said that it is "totally his decision," he said, "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 [decision]."

But CBS News chief White House correspondent Major Garrett reports Mr. Trump met with Jackson in the Oval in the afternoon, and Jackson said he wanted a chance to defend himself in public -- meaning getting a hearing. The president promised to back him up.

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Garrett says Jackson believes he has a story to tell and that he could advocate for the Trump agenda at the VA and have the president's direct backing to tame the bureaucracy -- and some administration officials agree.

Senate Majority Leader McConnell, R-Kentucky, wouldn't weigh in on Jackson's nomination at a weekly Senate press conference Tuesday. In response to a question posed by CBS News' Nancy Cordes regarding the nomination and the White House vetting process, McConnell said, "I'm waiting to hear from both Chairman Isakson and from the administration what they believe the way forward should be, and we'll take our cues from them."

On Tuesday, senators expressed concern about the White House vetting process, after the Veterans' Affairs Committee announced it was delaying Jackson's confirmation hearing.

He would be replacing David Shulkin, whom the president fired last month. Senators Johnny Isakson, R-Georgia, and Jon Tester, D-Mont., the top lawmakers on the committee, released a joint statement saying that the hearing had been postponed "in light of new information presented to the committee."

Their statement went on to say, "We take very seriously our constitutional duty to thoroughly and carefully vet each nominee sent to the Senate for confirmation. 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."

Isakson and Tester sent a letter to President Trump Tuesday requesting all information regarding any improper conduct pertaining to Jackson's service in the White House Medical Unit and as physician to the president.

"This incident does raise questions about the White House vetting process," Sen. Susan Collins, R-Maine, said Tuesday. It seems that these issues arose after he was nominated and were brought to the committee."

CBS News' Ed O'Keefe reported that accusations made by current and former employees involve a "hostile work environment" and include "excessive drinking on the job" and "improperly dispensing meds," according to one of the people familiar with the accusations, who was granted anonymity to speak frankly about the situation. Other people familiar with the stories also confirmed those details.

Jackson, who is making the rounds on Capitol Hill, told reporters he's "looking forward to rescheduling the hearing and getting the process moving." He promised, "I can answer the questions, absolutely."

Collins said that the allegations "that have come out against Admiral Jackson are "very disturbing." Beyond the accusations, though, Collins also said, "There is a second issue with Admiral Jackson: that is whether or not he has sufficient experience to manage the second largest department in the federal government."

Sen. Richard Blumenthal, D-Connecticut, who sits on the Veterans' Affairs Committee, told reporters Tuesday that lawmakers first learned of the allegations late last week, and they're seeking the FBI background check.

"The White House has been consistently and abysmally careless, even derelict in the vetting process, which accounts for some of the problems with their nominees," he said. "These very serious questions about Admiral Jackson need answers, and the answers should have been ready well before the questions were raised publicly. And that's a disservice to the nominee, as well as the American people."

CBS News' Alan He, Ed O'Keefe and John Nolen contributed to this report.