“I’d like to think that there’s a way we could fix [it] so that our service members do not have legal problems overseas, while still protecting the rights of the 9/11 victims,” said House Speaker Paul D. Ryan (R-Wis.), who backed the bill in public statements though he did not cast a vote during Wednesday’s override.

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Some lawmakers have advocated making changes to the measure during the post-election “lame duck” session, but Ryan said he didn’t know when the issue may be addressed.

Senate Majority Leader Mitch McConnell (R-Ky.) said Thursday the law could have “unintended ramifications” and needed “further discussion.” But he blamed the White House for not making a forceful argument about the threat posed by the legislation to to U.S. officials.

“Everybody was aware of who the potential beneficiaries were, but nobody had really focused on the potential downsides in terms of our international relationships,” said McConnell, who voted to override the president’s veto.

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Their comments infuriated White House officials who contend the dangers posed by the bill were obvious and articulated well ahead of the votes to pass the bill and then to override the veto.

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White House spokesman Josh Earnest said lawmakers’ recent comments are a “deeply embarrassing” display of “rapid-onset buyer’s remorse.”

“The suggestion on the part of some members of the Senate was that they didn’t know what they were voting on, that they didn’t understand the negative consequences of the bill,” he said Thursday. “That’s a hard suggestion to take seriously.”

The White House has warned the legislation is too broad and could set a dangerous precedent, inviting other nations to respond by suing American diplomats, military personnel and other officials in foreign courts over U.S. foreign policy actions.

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While the bill is intended to aid 9/11 victims’ families pursuit of Saudi Arabia through the court system, it is broader than that and would allow courts to waive claims to foreign sovereign immunity in situations involving acts of terrorism on U.S. soil.

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Before the Senate finished voting 97-1 Wednesday to override Obama’s veto, over two dozen senators signed a bipartisan letter indicating their intention to advance after the election legislation to blunt the measure’s impact if other countries try to retaliate. Senate Majority Leader Harry Reid (Nev.) was the only Democrat to side with the administration.

The House voted 348-77 to override Obama’s veto, with 59 Democrats and 18 Republicans supporting the president.

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Many lawmakers who had concerns about the bill complained this week that the White House was not putting much effort into lobbying to sustain Obama’s veto.

The president “is playing no role in anything,” said Senate Foreign Relations Committee Chairman Bob Corker (R-Tenn.), one of the lead senators agitating for changes to the measure.

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In the days leading up to the override vote, the White House, national security officials, the European Union’s delegation to the United States and business leaders urged lawmakers to sustain the veto. They warned the law will damage relations with Saudi Arabia and encourage other countries to pass laws that would allow them to target U.S. officials.

“All of that communications was made public before Congress passed the first vote to put this bill into law yesterday,” Earnest said. “Ignorance is not an excuse, particularly when it comes to our national security and the safety and security of our diplomats and our service members.”

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Lawmakers dismissed Earnest’s criticisms.

“The outburst yesterday from the White House over what happened is remarkable when they wouldn’t even sit down to meet with the secretary of state and us, to try to create to a solution to a problem they felt was real,” Corker said.

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Democrats, despite sharing frustration on the outcome of the vote, did not place the blame squarely in Obama’s lap.

“I share Senator Corker’s frustration on JASTA,” Senate Foreign Relations Committee ranking member Ben Cardin (D-Md.) said, referring to the bill by its acronym. But he faulted “circumstances that neither he nor I could control, nor could the administration control – and that is the timing of JASTA required us to take the veto override before the recess.”

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Cardin is one of many senators who wanted to see the veto override delayed until after the election, so lawmakers with concerns could have more opportunity to hash out a compromise with the White House.

Bill sponsors Sens. Charles E. Schumer (D-N.Y.) and John Cornyn (R-Texas) have said they are open to reviewing proposals. So far, however, they have dismissed the chief alternative – a measure that would have limited the measure to allow suits related to 9/11 alone – as “unacceptable.”

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Even Democratic leaders who supported the bill expressed regrets Thursday that more had not been done ahead of time to create an alternative.

“I do think perhaps it could have been written in a little bit of a different way,” said House Minority Leader Nancy Pelosi (D-Calif.), noting that about 60 Democrats voted to sustain the veto. “It’s a very sad situation.”

Mike DeBonis, Paul Kane, and Karen DeYoung contributed to this report.