U.S. lawmakers expressed doubts on Thursday 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 the Democratic president 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.