The Senate voted 58-40 in favor of proceeding to debate on the Veterans Job Corps bill, but the bill needed 60 votes to advance.
Sen. Jeff Sessions, R-Ala., argued in opposition to the bill, saying it would violate a congressional deal reached in 2011 on spending limits. The bill's sponsor, Sen. Patty Murray, D-Wash., said its cost -- $1 billion for five years -- was offset by revenues, The New York Times reported.
"It's unbelievable that even after more than a decade of war, many Republicans still will not acknowledge that the treatment of our veterans is a cost of war," Murray said in a statement following the vote.
The White House issued a statement accusing Republicans of blocking "a common sense plan to create the Veterans Jobs Corps and put tens of thousands of veterans back to work."
The statement said the administration has worked with congressional Democrats and Republicans to help veterans find jobs."
"We passed tax credits to encourage employers to hire veterans and released new tools to connect veterans with employers," the statement said.
"But we can do more and Senate Republicans should not block legislation that includes many of their ideas and stand between veterans and good jobs protecting and preserving America," the White House said.