Sens. Lindsey Graham and John McCain on Wednesday unveiled their “fix” to a controversial new law intended to allow families of victims of the September 11, 2001, terrorist attacks to sue Saudi Arabia.

Under their proposal, foreign governments would only be held liable for terrorist attacks “if they knowingly engage with a terrorist organization directly or indirectly, including financing,” as Graham explained. The fix is intended to narrow the law’s scope and reduce the likelihood that it would produce retaliatory suits against the United States.

Congress voted overwhelmingly in September to override a presidential veto of the law, called the Justice Against Sponsors of Terrorism Act, or JASTA, which the Obama administration warned would have unintended consequences.

Many members of Congress in both parties agreed the measure could have negative repercussions and have vowed to amend it. The concern is that allowing U.S. citizens to sue foreign governments over terrorist attacks could erode the concept of “sovereign immunity” and encourage other countries to file retaliatory lawsuits against the United States.

Passing any fix to the law during the lame duck session would require the unanimous consent of all 100 senators, a tall order considering Congress hopes to recess next week for the rest of the year. Don Stewart, a spokesman for Senate Majority Leader Mitch McConnell, said it was too early to say whether a fix for the measure would come up next year.

In a floor speech, Graham and McCain said they’re worried JASTA could pave the way for other countries to sue the United States over its drone strikes.

“If we don’t make this change, here’s what I fear — that other countries will pass laws like this, and they will say that the United States is liable for engaging in drone attacks or other activity in the war on terror and haul us into court as a nation,” Graham said. “I don’t want any nation state, including ours, to be sued for a discretionary act unless that discretionary act encompasses knowingly engaging in the financing or sponsorship of terrorism whether directly or indirectly.”

He added that he was trying to work with Sens. John Cornyn (R-Texas) and Chuck Schumer (D-N.Y.), the lead sponsors of JASTA, to get support for the fix.

After September’s veto override, McConnell acknowledged the law could have “unintended ramifications,” putting some of the blame on the White House for what he said was a “failure to communicate early about the potential consequences.”

House Speaker Paul Ryan (R-Wis.) has also signaled a willingness to revisit the law.

Following Graham and McCain’s floor speeches, a group advocating for the law issued a statement blasting the two senators’ proposed fix. The group, 9/11 Families and Survivors United for Justice Against Terrorism, said the provision would “effectively gut” JASTA.

“In April of this year, Senator Graham met with 9/11 family members from the September 11 Advocates Group and told them that he supported our cause 100 percent,” said Terry Strada, the group’s national chair. “Senator Graham is now stabbing the 9/11 families in the back. He and Senator McCain are seeking to torpedo JASTA by imposing changes demanded by Saudi Arabia’s lobbyists. We have reviewed the language, and it is an absolute betrayal.”

One congressional aide familiar with the changes being pushed called the provision “a giveaway to K Street lobbyists and the Saudis.”

Seung Min Kim contributed to this report.