Senate Majority Leader Republican Mitch McConnell (R-Ky.) said Tuesday the Senate will hold an override vote on a bill to give the families of 9-11 victims a chance to sue Saudi Arabia once President Obama vetoes it. EPA/MICHAEL REYNOLDS

Senate Majority Leader Mitch McConnell on Tuesday said he expects the Senate will successfully override President Obama’s expected veto of a bill that would allow the families of 9/11 victims to sue Saudi Arabia over its alleged support for the terrorists who carried out the attacks.

The White House has said the president intends to veto the bill, which it has until Friday night to do. McConnell (R-Ky.) said the Senate would act soon after.

“At whatever point the president vetoes it, we will have to take it up, and there will be a roll call vote on the veto override,” McConnell told reporters. “Our assumption is that the veto will be overridden.”

The bill would give courts the right to waive claims to foreign sovereign immunity in cases involving terrorist acts on U.S. soil.

The timing of the veto could be crucial. If lawmakers head home this week before the official veto, then it would buy the White House more time to negotiate a possible compromise that would allay concerns that the legislation is too broad in scope and would open the door to foreign governments dragging U.S. officials into courts over, for example, events from the wars in Afghanistan and Iraq.

But it now appears that Congress will be in session next week as negotiations on a stop-gap spending bill continue to drag on.

“I think JASTA’s a fait accompli if it happens over the next week,” Senate Foreign Relations Committee Chairman Bob Corker (R-Tenn.) told reporters Tuesday, referring to the bill by its official acronym. “My message to the caucus is going to be, unless there are 34 people willing to fall on their swords over this, it’s probably not worth falling on your sword over.”

The admission is striking, considering that Corker was one of the members hoping to buy more time for negotiations with the White House. The bill’s scope was already winnowed once earlier this year to accommodate concerns raised by the White House and some lawmakers about a diplomatic backlash.

The comments from McConnell and Corker come as an increasing number of senators are expressing doubts about the bill for reasons similar to those expressed by the White House.

“I am having second thoughts about it because I think it launches a number of unforeseen happenings,” said Senate Intelligence Committee ranking member Dianne Feinstein (D-Calif.), who added that “the message has been sent to Saudi Arabia” and the Saudi government “is trying to make a number of changes.”

“I think that moving ahead with violating a nation’s autonomy in this way is a mistake,” Feinstein added. “So I hope that it can be put off, and cooler heads will prevail.”

But Corker says he sees no signs from the White House that it is putting a full effort behind getting Congress to delay the vote and he has seen no proposals from the administration that could jump-start last minute negotiations.

“If for some reason the vote takes place in November instead of now, if in fact the administration has been able to come forth with something that’s different – but we just haven’t heard that,” Corker said. “I don’t feel any energy around this issue coming from the White House as far as trying to work on a solution they think will work.”