Veterans Affairs Secretary Eric Shinseki testified before the Senate Thursday on VA health clinics allegedly covering up treatment delays. (The Washington Post)

Updated 3:47 p.m.

Veterans Affairs Secretary Eric K. Shinseki vowed Thursday to remain in office until President Obama tells him to go, but lawmakers made clear that their patience is wearing thin and that they will be keeping close tabs on how the Department of Veterans Affairs responds to allegations of treatment delays and cover-ups at veterans medical centers.

Shinseki faced several hours of grilling during a Senate Veterans Affairs Committee hearing from Democratic and Republican senators who repeatedly expressed outrage and concern about the situation at a medical center in Phoenix and elsewhere. Beyond the hearing room, there was no groundswell calling for Shinseki's departure, but on the campaign trail, Republican congressional candidates began raising concerns about Shinseki, signaling that the allegations could quickly become a drag on Democratic attempts to maintain control of the U.S. Senate in the midterm elections.

Sen. Johnny Isakson (R-Ga.), a member of the Veterans Affairs panel, expressed tenuous support for Shinseki. "I like Eric an awful lot, but I can't believe the lack of knowledge of some of the things that were obvious and apparent within the system," he said. "He’s either been ill-served by his senior leadership – which I think is part of the systematic problem – or has been oblivious to what’s been going on around him."

Sen. Richard Blumenthal (D-Conn.), another member of the committee, asked Shinseki during the hearing whether the FBI should be leading the investigation of allegations that VA employees doctored official documents or destroyed evidence of secret records of patients awaiting care.

The FBI instead of the VA inspector general should take the lead, Blumenthal suggested, because the department's watchdog "lacks the resources, the authority and the expertise to do a criminal investigation. The more I hear, the more convinced I am that there’s very credible evidence of falsification of documents, destruction of evidence."

Blumenthal has called on Shinseki to hire "a new management team" but said he would withhold judgment on the secretary until a department-wide audit is complete. He dismissed suggestions that the scandal could become a factor in upcoming elections.

"I don't think this is a partisan issue," he said. "The problems at the VA have been tragic and long-standing and endemic to that agency."

Majority Leader Harry M. Reid (D-Nev.) agreed, saying that Shinseki has been leading a department plagued by decades of mismanagement and insufficient resources.

"Ten years ago or so, veterans' health care was a hiss and a byword. Now it's a pretty good system," Reid told reporters. "People look at it as really a measure of how we should take good care of people, and we need that to continue."

Minority Leader Mitch McConnell (R-Ky.) again stopped short of calling for Shinseki's resignation Thursday, but sought to tie the VA's problems to other missteps by the Obama White House.

"My concern is that the Obama administration will treat this scandal like it does all the others: Like a political crisis to get past rather than a serious problem to be solved," McConnell said, adding later: "If the president is truly serious, he needs to treat these stories at least as seriously as he did the Obamacare Web site fiasco, when he pledged his complete attention and the full force of his administration to do whatever needed to be done."

Other Republicans took a sharper approach. Sen. John Cornyn (R-Tex.) has called for Shinseki's resignation, and on Thursday faulted the secretary for displaying "a dismissive attitude" about the problems during the hearing. "The VA will not continue to operate in no-man's land and there will be consequences if these reports are found to be true."

Cornyn is one of a handful of House and Senate Republicans who have called for Shinseki's ouster — but they were joined Thursday by GOP political officials and a handful of congressional candidates.

The chairman of the Republican National Committee, Reince Priebus, called for "an independent investigation" of the VA scandal. And Scott Brown — the former Republican senator from Massachusetts now running for a Senate seat in New Hampshire — repeated his calls for Shinseki's ouster: "We don't need another government commission. We don't need more excuses. This is not the time for business as usual. We need to clean house, starting at the top."

Rep. Bill Cassidy (R-La.), who is running for a Senate seat in his state, blasted Shinseki's performance Thursday. "What the VA has allegedly done is another example of what happens when the government controls health care," he said. "The system lines up to serve the bureaucrat — when the bureaucrat has the power, the patient suffers."

In Alaska, Republican Senate candidate Brian Sullivan — who serves as a lieutenant colonel in the U.S. Marine Corps Reserve — said in a statement that he has "utmost respect" for Shinseki but that he should step down. The accusations of poor care "undermines America’s sacred commitment to our men and women who have fought and sacrificed for our country," Sullivan said. "Leadership and accountability are what’s needed now. We have neither at the VA, and that needs to change."

Brown, Cassidy and Sullivan are running in two of the most competitive Senate races this year, but the Democratic incumbents they are challenging — Jeanne Shaheen (N.H.), Mary Landrieu (La.) and Mark Begich (Alaska) — have so far not called for Shinseki's ouster.