A major defense-spending bill hit an unexpected bump on its journey through the U.S. Senate over an amendment on veterans’ gun rights, which devolved into a heated floor debate and foreshadows a potential battle over Democrats’ vows to tweak the filibuster rules in the clubby, traditionally collegial body.

Sen. Tom Coburn, Oklahoma Republican, wants veterans who have been deemed “mentally incompetent” to have their cases adjudicated by a judge — rather than the Department of Veterans Affairs, as happens currently — and argued that veterans who simply cannot support themselves financially are needlessly given the label and, as such, cannot buy or possess firearms.

“We’re not asking for anything big,” Mr. Coburn said Thursday evening on the Senate floor. “We’re just saying that if you’re going to take away the Second Amendment rights … they ought to have it adjudicated, rather than mandated by someone who’s unqualified to state that they should lose their rights.”