Congress may override President Barack Obama's veto of the Justice Against Sponsors of Terrorism Act. Getty Images

The U.S. Senate could override President Barack Obama’s veto for the first time during his administration Wednesday as the legislative and executive branches battle over the bill that would allow families of 9/11 victims to sue nations believed to be harboring terrorists.

The Senate, followed by the House of Representatives later this week, is scheduled to resume its session Wednesday morning and was scheduled to start two hours of debate at 10 a.m. EDT over the Justice Against Sponsors of Terrorism Act, or JASTA, before voting on whether to override Obama’s veto.

The Obama Administration, as well as many foreign allies, have said the measure is harmful to the sovereignty of other nations and could even worsen foreign relations and U.S. appeal abroad.

However, JASTA proponents believe it’s a measure that will provide further justice to victims’ families. And even in a Congress that has faced heavy criticism for its failure to work together, JASTA received universal passage by both Democrats and Republicans. In May, the Senate passed the bill unanimously and earlier this month the House completed a resounding voice vote.

The bill has also received support from families of 9/11 victims who want nations like Saudi Arabia, where 15 of the 19 9/11 hijackers originated from, to be held accountable.

According to NPR, versions of the bill have bounced around Congress since roughly 2009, but it hadn’t reached the legislative floor until this year.

Lawmakers on both sides of the aisle have said publicly that they believe Obama’s veto will be overridden, which requires a minimum of two-thirds of the Senate and then the House, but some have also done some last-minute lobbying against the override.

Rep. Adam Smith, D-Wash., and Rep. Mac Thornberry, R-Texas — both members of the House Armed Services Committee and the latter being the chairman — issued a letter to lawmakers urging reconsideration, according to USA Today.

“We must work with other nations, even imperfect ones,” Thornberry wrote in the letter. “Requiring their government officials to participate in and give testimony in lawsuit —even when nothing has been proven— will create tensions and lead to less cooperation. I believe the net result will harm our security. ”