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In the wake of the Sandy Hook tragedy, Mr. Obama and other gun control advocates called for bans on military-style semi-automatic weapons and high-capacity ammunition magazines, but both of those proposals stalled early in the process. That left gun control advocates clinging to hope for enhanced background checks as the only significant gun restriction that might pass on Capitol Hill.

Sen. Joe Manchin III, West Virginia Democrat, and Sen. Patrick J. Toomey, Pennsylvania Republican, drafted compromise legislation that would have expanded the required checks to all sales online and at gun shows, while exempting such private transfers as gifts between family members or transactions between friends.

That measure failed in the Senate in April, and furious lobbying efforts have ensued on both sides of the issue.

Some senators have indicated that they want to take up a modified version by year’s end, but with an August recess and fall budget fight looming, it’s unclear whether another run at gun legislation will fit into the mix.