WASHINGTON — The Obama administration is running out of time and options to close the Guantanamo Bay detention center in Cuba, so officials are scrambling to release as many prisoners as possible and considering novel legal strategies that include allowing some men to strike plea deals by video-teleconference.

Another option would be to send others to foreign countries to be prosecuted. But it still looks to be too late to close the prison before President Barack Obama leaves office in January, denying him the chance to fulfill a campaign pledge.

There’s the difficulty in transferring prisoners from the U.S. base in Cuba, questions about the legality of plea deals and solid opposition in Congress to anything that might help Obama achieve his goal.

“The clock has struck midnight and the American people have won,” said Sen. Cory Gardner, R-Colo., who has said he would oppose any effort to move detainees to prison facilities in his state. “The president needs to admit that.”

Later this month, lawmakers are on track to extend a ban on moving detainees to U.S. soil. That would leave the president with no way to make the January 2017 deadline, barring an unexpected reversal in Congress or a politically explosive executive order.

The White House increasingly is pointing to a parallel strategy: trying to shrink the number of detainees in hopes of persuading lawmakers that Guantánamo is too expensive to sustain as a prison.

Of the 80 remaining detainees, 30 have been cleared for an overseas transfer. Most will leave starting in late June and continuing into July, according to a U.S. official.

Seven additional detainees are facing trial by military commission, including five charged with planning and supporting the Sept. 11 attacks. Three others have been convicted.

The remaining 40 were either at one time considered for prosecution or held as indefinite “law of war detainees” until the end of hostilities in the fight against terrorism that began after the 2001 attacks. The United States started using Guantánamo for suspects in January 2002; at its peak, the facility held about 680 prisoners.