 -- The White House slammed Congress for questioning the effects of a bill that would allow individuals to sue foreign governments after overriding President Obama's veto of the measure, saying that lawmakers were beginning to have "buyer's remorse" and saying that "ignorance is not an excuse."

Republican and Democratic representatives are now saying the measure, which will now allow families of 9/11 victims to sue Saudi Arabia for alleged involvement in the attacks, needs to be fixed.

“I think what we've seen in the United States Congress is a pretty classic case of rapid onset buyer's remorse,” White House Press Secretary Josh Earnest said in Thursday's briefing. “What's true in elementary school is true in the United States Congress -- ignorance is not an excuse.”

The bill in question is the Justice Against Sponsors of Terrorism Act, which the president vetoed but the House and Senate voted in overwhelming majorities to override for the first time in the administration’s history.

On Wednesday, Earnest called the override "the single most embarrassing thing the United States Senate has done” in over two decades.

After joining almost all of their colleagues to pass the bill Wednesday, a bipartisan group of 28 senators led by Foreign Relations Committee Chairman Bob Corker, R-Tenn., wrote to the top supporters of the bill, Sens. Chuck Schumer, D-NY and John Cornyn, R-TX, warning about “potential unintended consequences” of its passage.

“We would hope to work with you in a constructive manner to appropriately mitigate those unintended consequences,” the senators wrote.

Earlier Thursday, Senate Majority Leader Mitch McConnell blamed the White House for not doing enough to express its own concerns about the legislation to Congress.

“That was a good example, it seems to me, of failure to communicate early about the potential consequences of a piece of legislation that was obviously very popular,” he said. “I told the president that this was an example of an issue we should have talked about much earlier.”

But he also acknowledged that, in their zeal to support the families of 9/11 victims, lawmakers themselves did not fully consider the potential consequences of passing a bill that might leave the U.S. open to similar litigation.

“By the time everybody seemed to focus on the potential consequences of it, members had basically already taken a position,” he said. “Everybody was aware of who the potential beneficiaries were but no one had really focused on the potential downsides in terms of our international relationship.”

Earnest had a different characterization for what happened.

“The suggestion on this part of some members of the Senate is that they didn't know what they were voting for. They didn't understand the negative consequences of the bill. That's a hard suggestion to take seriously," Earnest said.

McConnell suggested that he would be open to considering changes to the JASTA bill once Congress returns after the November elections.

In the House, both Speaker Paul Ryan and House Minority Leader Nancy Pelosi also signaled some openness to revisiting the bill later this session.

“I do think that perhaps it could have been written in a little bit of a different way that addressed some of the concerns,” Pelosi said during her own press conference.

Schumer, one of the key advocates of the bill, said he was also open to making tweaks, but only to a certain point.

“It has to be something that doesn't weaken the bill and limit the right of these families to get their day in court and justice,” Schumer, the incoming Senate Democratic leader, said.