Sen. Tom Coburn (R-Okla.) speaks about veterans while flanked by Sens. Jeff Flake (R-Ariz.), left, John McCain (R-Ariz.) and Richard Burr (R-N.C.) during a news conference on Capitol Hill on Tuesday. (Mark Wilson/Getty Images)

In response to allegations of long wait times and inadequate service at Department of Veterans Affairs hospitals, four Republican senators introduced a bill Tuesday that would allow veterans to seek care outside the department's health-care system under certain conditions.

The Veterans Choice Act is co-sponsored by Sens. John McCain (Ariz.), Tom Coburn (Okla.), Richard Burr (N.C.) and Jeff Flake (Ariz.). The bill would give veterans a "choice card" that they could present at privately owned hospitals or clinics for care. It also would prohibit VA facilities from recording scheduling and wait-time metrics for the purpose of securing bonuses; require the VA secretary to outline penalties for falsifying data; and allow the secretary to remove any top career VA official for inadequate performance.

"It would empower veterans who can't schedule an appointment within a reasonable time or live too far away from the VA medical facility to exercise the choice — I emphasize the choice — of getting medical care from any doctor in a Medicare or TRICARE program," McCain, the lead sponsor, told reporters.

The proposal comes less than a week after Veterans Affairs Secretary Eric Shinseki resigned after it was revealed that veterans' facilities were chronically under reporting wait times and is one of a series of bills being filed by Democrats and Republicans in attempt to secure timely medical care for thousands of veterans who have experienced lengthy wait times for care.

Democrats are rallying around a comprehensive proposal by Senate Veterans’ Affairs Committee Chairman Bernard Sanders (I-Vt.). His Restoring Veterans’ Trust Act also would give the VA secretary the authority to remove senior officials based on poor job performance, as well as grant the department expedited hiring authority for nurses and doctors, and authorize it to lease 27 new facilities in 18 states and Puerto Rico, among other changes.

McCain insisted that his bill was superior to Sanders's proposal.

"Unlike Senator Sanders's bill, this legislation addresses the root causes of current VA scandal and empowers veterans with greater flexibility to get the quality medical care that he or she deserves," he said.

Senate Democrats also have not ruled out quickly passing a measure that would make it easier for the VA secretary to fire or demote senior managers found responsible for mismanaged or delayed care, according to senior aides familiar with potential plans. A similar measure easily passed the House almost two weeks ago.

Sanders's bill includes language permitting the VA secretary to move to fire or demote employees, but also allows those workers to appeal the decision to the Merit Systems Protection Board within seven days. The federal board that hears such appeals from workers would have to make a decision within 21 days.

The new legislative proposals come as a new Washington Post-ABC News poll released Tuesday found that 97 percent of Americans describe the problems at VA as serious, with 82 percent calling them "very serious."

About four in 10 Americans say the president deserves significant blame for the department's problems, while six in 10 say he personally deserves just some or none of the blame. Along partisan lines, roughly six in 10 Republicans say Obama was principally to blame, while three in five independents and four in five Democrats say most of the blame should go elsewhere.