WASHINGTON — A little-known provision of the Patriot Act, overlooked by lawmakers and administration officials alike, appears to give President Obama a possible way to keep the National Security Agency’s bulk phone records program going indefinitely — even if Congress allows the law on which it is based to expire next year.

Senate Republicans on Tuesday night used a filibuster to block consideration of a bill to end and replace the N.S.A. phone records program. The debate about what may happen next has played out based on a widely held premise: that the legal basis for the program, Section 215 of the Patriot Act, will expire on June 1, so if Congress remains gridlocked, the program will automatically shut down.

“I believe that if we do not pass this bill, the metadata program is at risk because the 215 program sunsets next year,” Senator Dianne Feinstein, Democrat of California, said in Tuesday night’s debate. But that premise may be incorrect. If the summer arrives and the program is facing a shutdown, Mr. Obama could invoke the provision to ask the Foreign Intelligence Surveillance Court to keep it going.

Several executive branch officials said the administration had not been studying that option and expressed doubt that Mr. Obama would take such a step, or that the Surveillance Court would agree to it if he tried. Still, the mere existence of a potential way for the program to keep going without congressional action could recast the debate.