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Less than a day after voting to override President Obama’s veto of a bill that would allow 9/11 families to sue Saudi Arabia, senior lawmakers expressed concerns Thursday over possible “unintended consequences” to the country’s national security and foreign policy.

After a historic and overwhelming rejection of the presidential veto, Republican leaders of the Senate and House of Representatives opened the door to fixing the bill's potential impact on national security.

Related: The 9/11 Victims' Bill is Now A Law — What's Next?

House Speaker Paul Ryan, R-Wisc., said Congress might have to fix the Justice Against Sponsors of Terrorism Act (JASTA) 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.

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The new 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.

White House Spokesmen Josh Earnest dismissed Congress’ attempt to blame the Administration for what he described as “rapid onset buyer’s remorse.”

“Within minutes of casting their vote to put that bill into law you had members of the U.S. Senate write a letter expressing deep concern about the potential impact of the bill they just passed,” Earnest said Thursday.

He went on to list a series of letters by former CIA officials, national security advisors, and European attorneys warning about the potential impact of the bill.

“Ignorance is not an excuse, particularly when it comes to our national security and the safety and security of our diplomats and service members,” he said.

Senator Mitch McConnell, R-Ky., said that the White House should have reached out early on to prevent a vote and later on a override to the bill.

“By the time everybody seemed to focus on the potential consequences (of the bill), members had already basically taken position,” McConnell said.

Related: Secret 28 Pages of 9/11 Report Released, Hold No Proof of Saudi Link

“Everybody was aware about who the potential beneficiaries were, but nobody really focused on the potential downside in terms of international relationships,” he said.

Trent Lott, a former Republican Senate Majority Leader who now lobbies in Washington for 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.