WASHINGTON -- If it could only be this easy: In a tone of bipartisanship that will not likely last, the Senate on Tuesday overwhelmingly advanced a $1 billion program proposed by President Obama to establish a Veterans Jobs Corps.

The procedural vote, coming on the 11th anniversary of the Sept. 11 terrorist attacks, was 95-1. Four senators did not vote. Both of the Bay State’s senators, Democrat John Kerry and Republican Scott Brown, voted in favor. Kerry and Brown are both known for their work on behalf of veterans.

Senator Rand Paul, a Republican from Kentucky, registered the only vote against the measure, which would give hiring preference to post-9/11 veterans for public works jobs, as well as openings in police and fire departments.

It was a rare victory for Obama. Many of his previous jobs initiatives have been rejected by House Republicans or their Senate counterparts, who have used the filibuster to block the packages.

The Veterans Jobs Corps would help put 20,000 veterans to work over five years on projects including restoring wildlife habitat and maintaining public lands.

The corps would also provide job centers from which veterans can search for work.

The legislation, authored by Senator Bill Nelson, a Florida Democrat running for reelection, would be hard to resist in an election year when both parties want to appear in the best light to a crucial voting bloc.

While Tuesday’s procedural vote allows the measure to be given an up-or-down vote, the fate of the bill remains uncertain because it is expected to be loaded with amendments, some of which could end up being deal killers.

The House is awaiting Senate action before it takes up the matter.