If passed, it would allow veterans more access to private doctors and give the VA new authority to open 26 clinics, hire more doctors and nurses and fire poor-performing staff.
It was reached after rare bipartisan negotiations led by Senator John McCain, a Republican, and Bernard Sanders, an independent who caucuses with the Democrats.
The scandal over widespread schemes to mask the long delays prompted allegations from VA doctors in Phoenix that 40 veterans had died while waiting for appointments at VA facilities there. Last week, it brought the resignation of Veterans Affairs Secretary Eric Shinseki.
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His replacement, VA Acting Secretary Sloan Gibson, told reporters in Phoenix that VA staff in recent days had contacted 1,700 veterans whose names appeared on secret waiting lists for care and found that 18 of them had already died.
Gibson said some of the 18 had initially contacted the VA for "end of life care" but he added that it was "inexcusable" that so many veterans were left languishing on a secret waiting list and vowed change.
"This is not what our veterans deserve; this will not stand," said Gibson, who joined the VA in February. "I will not be part of some effort to maintain the status quo here."
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Sanders, who chairs the Senate Veterans Affairs Committee, said lawmakers from both parties are "appalled" by the delays and cover-ups in Phoenix and elsewhere.
"We have a crisis on our hands and it is imperative that we deal with that crisis," Sanders said on the Senate floor.
The proposed legislation, targeted for a Senate vote next week, would authorize leases for 26 new major clinics in 18 states and use $500 million in leftover funds to hire new VA doctors and nurses to speed veterans' access to care.