Jerry Moran, R-Kan., on Tuesday.
Jackson's withdrawal came just a day after he indicated that he would fight on, telling reporters that his shock nomination was "still moving ahead as planned". "That should be pretty easy to prove".
Tester faces a potentially tough reelection this year in a state Trump won by 20 points in 2016.
The document, unveiled by Sen. And he reportedly provided a large supply of the prescription painkiller Percocet to a staffer in the White House military office.
The allegations in the committee summary have not been independently verified.
Several entities could potentially investigate Jackson.
He had been due to have a Senate confirmation hearing on Wednesday. That report may have been as damaging to Jackson's prospects among Republican senators as the more salacious allegations of drinking on the job.
Jackson on Thursday castigated the allegations as "completely false and fabricated" in a statement announcing his withdrawal. "He is a tremendous asset to the entire White House team".
Trump scoffed at that concern, saying, "You could run the biggest hospital system in the world and it's small time compared to the Veterans Administration". He specializes in emergency medicine and served with a battlefield surgical unit in Iraq.
His prior nominees for labor secretary, Army secretary and Navy secretary all withdrew previous year after questions arose during their vetting process.
Trump will not be deterred, said Scalise.
"I want to thank the service members who bravely spoke out over the past week. It's too ugly and too disgusting".
The upset was the latest chaotic personnel decision to rock Trump's White House, which has been roiled by an unusually high number of firings and resignations.
"Under VA's new leadership, which is now firmly aligned with President Trump and his priorities, the department's operations have improved in many ways", the release stated.
Jackson had met with White House officials Wednesday evening, a senior official says, according to CBS News' Major Garrett, but did not discuss withdrawing his nomination. Additionally, it reveals that President Trump's vetting process (if there is one) is not working.
The White House, which was criticized for failing to adequately vet Jackson's nomination, defended him until the end, saying that his record as a physician serving three presidents was unassailable, and demanding that he be allowed to defend himself during a confirmation hearing. "So nobody has experience, you know, it's a big monster". "Dr. Ronny Jackson was not qualified to run the VA. I'm fed up with these political games from Tester and his blind allegiance to his party bosses and not the people of Montana".
But the top Democrat on the same committee as Roe said it was time for Jackson to bow out of further consideration.
Jackson denied numerous allegations in his statement - "The allegations against me are completely false and fabricated", he said - but announced that he was "regretfully withdrawing my nomination to be Secretary for the Department of Veterans Affairs". And that was before accounts of questionable behavior on Jackson's part emerged.
Mr Trump's first veterans affairs secretary, David Shulkin, was dismissed after an ethics scandal and mounting rebellion within the agency.
The move coincided with Trump's removal of Shulkin as VA secretary. Prior to joining FCW, Mazmanian was technology correspondent for National Journal and served in a variety of editorial roles at B2B news service SmartBrief. Numerous large veterans service organizations are wary of what they see as a push toward privatization.
"Washington's a mess, but that's not stopping me from getting bills to help Montana signed into law by President Trump", Tester says in the ad. "What does he need it for?" If the conclusions of an investigation are serious, the military also in rare cases can demote officers as it forces them out of the military. It said Jackson was called "Candyman" because he would provide whatever prescriptions staff sought without paperwork.