WASHINGTON — After two overwhelming votes in two days, members of Congress say they are confident they can agree on a bill to improve veterans’ health care and send it to the president’s desk by the end of the month.

The Senate easily approved a bill Wednesday to help shorten wait times for thousands of military veterans seeking medical care, a day after the House unanimously adopted a similar measure.

The Senate bill would authorize about $35 billion over three years to pay for outside care for veterans, as well as hire hundreds of doctors and nurses and lease 26 new health facilities in 17 states and Puerto Rico. The House would spend about $620 million over the same period.

Just three lawmakers — all Republican senators — voted against the veterans measures, compared with 519 lawmakers who voted in favor.

Opponents said the Senate bill was a “blank check” to spend billions of dollars with little or no way to rein it in.