After last week’s shooting deaths of nine people at a black church in Charleston, S.C., Senate Minority Leader Harry Reid (D., Nev.) said Tuesday he is considering a maneuver to force lawmakers to take a side on the expansion of background checks, a major priority of gun safety groups but widely considered a political nonstarter.

On the Senate floor, Mr. Reid enumerated recent mass shootings, from a movie theater in Aurora, Colo., to an elementary school in Newtown, Conn. “We can do something about this sad, violent reality,” Mr. Reid said. “We can expand, for example, background checks for people wanting to buy guns … is that asking too much?”