Senior senators are working on a new plan to address concerns at the Department of Veterans Affairs with hopes of striking a bipartisan deal in the coming days that would help address long wait times for veterans seeking medical care at government-run facilities.

Word of a possible deal first came Wednesday morning when the Senate Veterans Affairs Committee abruptly cancelled plans to hold a hearing on one possible proposal Thursday. The comprehensive proposal by the committee's chairman, Sen. Bernie Sanders (I-Vt.), would allow the VA secretary to fire or demote senior officials, authorize the department to enter into leases for more than two dozen new facilities and provide further tuition assistance to younger veterans.

Senate Veterans Affairs Committee Chairman Bernie Sanders (I-Vt.)  speaks with Sen. Tammy Baldwin, (D-Wis.) as they take an escalator to the Senate Chamber on Capitol Hill on Wednesday. (J. Scott Applewhite/AP)

But Sen. John McCain (R-Ariz.) and other Republican senators this week unveiled a competing plan that also would allow the VA secretary to dismiss poor-performing workers, but focuses primarily on allowing eligible veterans to seek medical care outside the VA system.

With very few substantial differences between the two measures — and with a new Washington Post-ABC News poll showing near-unanimous national concern about the VA's troubles — senators now appear more eager to quickly strike a deal.

“In this extremely partisan facility there is at least a sense of urgency to address the issue of the veterans,” McCain told reporters.

He and Sanders declined to share specifics of their talks.

But Sanders said he hoped to reach a deal in the coming days. "The issue is how can we make sure that every veteran in this country can get into a VA facility in a reasonable period of time. And if they can't, what do they do?" he said.

In a sign of how quickly lawmakers might move to reach an agreement in the Senate and send legislation over to the House, Rep. Jeff Miller (R-Fla.), chairman of the House Veterans Affairs Committee, spent several hours on the Senate side of the U.S. Capitol Wednesday in meetings with GOP senators and Sanders.

"This is a recess period for the House, but it's important enough for the chairman of the committee to be here," he told reporters.

Any agreement passed by the Senate must focus on patient wait times and access to facilities and ensuring that VA officials can be fired or demoted for poor performance, he said.

The new talks came amid reports that the White House has approached the Cleveland Clinic’s chief executive, Delos “Toby” Cosgrove, a doctor and Vietnam War veteran, about serving as the new VA secretary.

The news caught multiple senators of both parties and senior aides by surprise, with virtually everyone saying that they first learned about the overtures to Cosgrove in news reports.

Sen. Rob Portman (R-Ohio), who has known Cosgrove for several years, said he hadn't spoken with the medical executive about the possibility of joining the Obama administration, but praised him as a potentially solid pick.

“He’s a very competent guy and in particular he is good at health-care delivery, which is one of their great challenges at the VA," Portman said. "Cleveland Clinic is not only a premier research organization, it also provides very efficient health care — having been there with one of my family members and having talked to Toby as well as many other people about their quality initiatives, safety initiatives, and just efficiency. The cost of health care is one of their big focus points. He would bring a lot to the table."

Sen. Richard Burr (R-N.C.), ranking Republican on the veterans committee, would only offer that the next VA secretary "just needs to be somebody who has great management skills." And Sen. Mark Kirk (R-Ill.) said that several GOP senators had joked that retiring Sen. Tom Coburn (R-Okla.) should be nominated for the position.

"He'd be a great guy to really whip the culture of corruption inside the VA," Kirk said. "We all kind of had a laugh about it — let's send Tom in there since he's retiring."

Kirk added that he also likes VA Acting Secretary Sloan D. Gibson: "I like him as a person, because I'd heard of him before he got the job," he said.

No matter what kind of legislation emerges in the coming days, or whoever President Obama picks as his new VA secretary, the department's troubles will be the subject of sustained congressional oversight in the coming weeks.

Miller said that his committee will hold another hearing Monday evening to hear testimony from the VA Inspector General and the Government Accountability Office on their initial investigations into allegations of delayed wait times and other mismanagement at a VA medical center in Phoenix.

"We're going to have two hearings a week for the foreseeable future," he said.