Washington – The Senate rejected an effort Wednesday to expand the use of firearms on some of the nation's most frequently visited federal lands, handing gun control advocates a modest success.

The measure, backed by the National Rifle Association, represented one of two efforts Wednesday by gun rights supporters to take the offensive in Congress. Across the Capitol, a Republican-run House committee voted to make it easier for some veterans with mental difficulties to get firearms.

The Senate proposal would have let people use guns for any legal purpose on lands managed by the Army Corps of Engineers, which oversees nearly 12 million acres that abound in lakes, rivers, campsites and hiking trails. Gun use on those properties is limited such activities as target shooting and hunting.

Senators voted 56-43 for the proposal by Sen. Tom Coburn, R-Okla., but it fell short of the 60 votes needed for passage.

Eleven Democrats and one Democratic-leaning independent voted for Coburn's plan, underscoring the party's divisions on the issue.

Those voting for Coburn's proposal included all four Democrats who opposed the bipartisan bill expanding federal background checks to more gun buyers that the Senate rejected three weeks ago.

The background check expansion has been the pillar of President Obama's effort to restrict guns after December's elementary school massacre in Newtown, Conn. Top Democrats and other supporters hope to win fresh support and get a new vote on background checks, perhaps next month. Advocates hope that voting for Coburn's proposal might let some senators show voters they support gun rights and give them more leeway to reverse themselves and vote for background checks next time.

Also backing Coburn's proposal were the two authors of the defeated background check measure, Sens. Joe Manchin, D-W.Va., and Patrick Toomey, R-Pa.

Sen. Mark Kirk of Illinois, a supporter of the Manchin-Toomey plan, was the only Republican to vote against the measure.

Also Wednesday, the House Veterans Affairs Committee voted by voice to require a judge or magistrate to declare a veteran is dangerous before the person's name is entered in the background check system's database of those forbidden from getting firearms.

Currently, the Veterans Affairs Department sends the system the names of veterans it has declared unable to manage their financial affairs — 127,000 names since 1998.