U.S. lawmakers on Thursday expressed doubts about Sept. 11 legislation they forced on President Barack Obama, saying the new law allowing lawsuits against Saudi Arabia could be narrowed to ease concerns about its effect on Americans abroad.

A day after a rare overwhelming rejection of a presidential veto, the first during Obama’s eight years in the White House, the Republican leaders of the Senate and House of Representatives opened the door to fixing the law as they blamed Obama, a Democrat, for not consulting them adequately.

“I do think it is worth further discussing,” Senate Majority Leader Mitch McConnell told reporters, acknowledging that there could be “potential consequences” of the “Justice Against Sponsors of Terrorism Act,” known as JASTA.

House Speaker Paul Ryan said Congress might have to “fix” the legislation to protect U.S. troops in particular.

Ryan did not give a time frame, but Republican Senator Bob Corker, chairman of the Senate Foreign Relations Committee, said he thought JASTA could be addressed in Congress’ “lame-duck” session after the Nov. 8 election.

The law grants an exception to the legal principle of sovereign immunity in cases of terrorism on U.S. soil, clearing the way for lawsuits by the families of victims of the attacks seeking damages from the Saudi government. Riyadh denies longstanding suspicions that it backed the hijackers who attacked the United States in 2001. Fifteen of the 19 hijackers were Saudi nationals.

Riyadh is one of Washington’s longest-standing and most important allies in the Middle East and part of a U.S.-led coalition fighting Islamic State militants in Iraq and Syria.

JASTA will add tension to U.S.-Saudi relations, after friction over Obama’s 2015 nuclear deal with Saudi rival Iran, but it is not expected to have a lasting effect on a relationship with advantages for both countries.

The Saudi-U.S. relationship has endured “multiple times of deep outrage” over 70 years, said Thomas Lippman, a Saudi Arabia specialist at the Middle East Institute.

“The two countries need each other as much today as they did before the day before yesterday,” Lippman said.

‘Rapid Onset Buyer’s Remorse‘

White House spokesman Josh Earnest mocked lawmakers for shifting “within minutes” from overwhelmingly voting to override the veto to wanting to change the law.

“I think what we’ve seen in the United States Congress is a pretty classic case of rapid onset buyer’s remorse,” Earnest told a White House briefing.

Corker criticized the White House, saying he had tried to work with the administration to find a compromise before the veto override, but the administration declined a meeting.

Democratic Senator Chuck Schumer, who championed JASTA in the Senate, said he was open to revisiting the legislation.

“I’m willing to look at any proposal they make but not any that hurt the families,” he said at a news conference.

However, he said he would oppose a suggestion that the measure be narrowed to only apply to the Sept. 11, 2001, attacks.

“You know what that does? It tells the Saudis to go ahead and do it again, and we won’t punish you,” Schumer said.

Corker said another suggestion was establishing an international tribunal so experts could determine whether there was culpability, and that the Saudis had been willing to sit down and work on a compromise.

“Never in their conversations has there been any kind of threat,” he said. “They are making observations about where this could lead. We’ve had other Arabs in the region weigh in and express concerns.”

Trent Lott, a former Republican Senate Majority Leader now at a Washington law firm lobbying for the Saudis, said attorneys would look carefully at JASTA’s language.

“I do feel passionately this is a mistake for a variety of reasons, in terms of threats to troops, diplomats, sovereignty, there’s serious problems here. Hopefully we can find a way to change the tenor of this,” Lott said.

(Additional reporting by Roberta Rampton, Susan Cornwell, David Morgan, Yara Bayoumy, David Alexander and Susan Heavey.)