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But Republican amendments also could attract on-the-fence senators who represent gun-friendly states and make the background check amendment — already facing problems attracting the 60 votes necessary to avert any filibuster — that much more difficult to pass.

The background check amendment carves out exemptions for private transactions between family members and friends. Presently, only federally licensed dealers are legally required to perform the checks.

A total of 68 senators voted to bring the bill to the Senate floor for debate, including 16 Republicans. But of those GOP members, just four have indicated they could support the Manchin-Toomey background check proposal, while 11 have said they will oppose it.

Sen. Kelly Ayotte of New Hampshire has not signaled publicly whether she will vote for it.

Several Democrats also could vote against the background check compromise, which — combined with the GOP objections — would leave the measure shy of the 60 votes needed.