WASHINGTON — On Wednesday, Congress was so determined to pass a law to sue Saudi Arabia that it overrode President Barack Obama’s veto. But possible backlash against America had top Republican leaders looking for someone else to blame Thursday.

And they appear to have settled on Obama.

The Justice Against Sponsors of Terrorism Act allows victims of the 9/11 attacks to sue the kingdom for its alleged, but unproven, support of the hijackers who flew planes into the World Trade Center and the Pentagon.

Opponents had argued that the bill was caving in to conspiracy theorists and that it would raise the specter of other nations hauling the United States into court for things it actually does — such as killing civilians in drone strikes. The White House called the override the “single most embarrassing thing that the United States Senate has done” in decades.

Even 28 lawmakers who had just helped to pass the first override of Obama’s presidency sent a letter to their own leaders Thursday saying maybe there should be changes.

So Senate Majority Leader Mitch McConnell (R-Ky.) leveled at least partial blame on Obama.

“That was a good example, it seems to me, of a failure to communicate early about the potential consequences of a piece of legislation,” McConnell told reporters before Congress got out of town until after the elections. “By the time everybody seemed to focus on some potential consequences of it, members had already basically taken a position.”

“I think it was just a ball dropped,” McConnell added. “I wish the president — I hate to blame everything on him, and I don’t — but it would have been helpful had he, uh, we had a discussion about this much earlier than last week.”

Senate Republican Whip John Cornyn (R-Texas), a sponsor of bill, was harsher on Wednesday, while his colleagues were working up their letter expressing doubts.

“What’s so remarkable to me is the detachment of this White House from anything to do with the legislative process,” Cornyn told reporters. “They were basically missing in action during this whole process.”

But there’s a catch.

Before criticism started blowing up around the world over JASTA, Republicans accused Obama of doing too much to kill the bill they are now worried about. And Cornyn in particular was angry about it. He said so in April, on the Senate floor, just before Obama went to meet with the Saudis.

“Unfortunately, the administration has worked to undercut progress of this legislation at every turn,” Cornyn said.

“It appears that the Obama administration is pulling out all the stops to keep this bill from moving forward before the president’s visit to Riyadh,” he said. “I wish the President and his aides would spend as much time and energy working with us in a bipartisan manner as they have working against us trying to prevent victims of terrorism from receiving the justice they deserve.”