President Obama: Congress Made 'Mistake' Overriding His Veto of 9/11 Bill

— -- President Obama said Congress made a "mistake" in overriding his veto of a bill that would allow the families of 9/11 victims to sue Saudi Arabia for its alleged role in the terrorist attacks.

"It was a mistake," the president said during CNN's "Presidential Town Hall" in Fort Lee, Virginia today. "If we eliminate this notion of sovereign immunity, then our men and women in uniform around the world could potentially start seeing ourselves subject to reciprocal laws."

"This is a dangerous precedent and it's an example of why sometimes you have to do what's hard. And, frankly, I wish Congress here had done what's hard," the president said.

He went on to describe why he believes the move was a "political vote."

"If you're perceived as voting against 9/11 families right before an election, not surprisingly, that's a hard vote for people to take," Obama said. "But it would have been the right thing to do."

The Senate today voted 97-1 to override the president's veto, while the House voted to override by a large margin: 348-77 and one present vote. The votes cemented the first veto override for Obama of his eight years in office.

Some lawmakers have sided with the White House in expressing concerns about the bill, but that has not been enough to overcome the widespread congressional support for the bill.

"I look forward to the opportunity for Congress to override the president’s veto, provide these families with the chance to seek the justice they deserve and send a clear message that we will not tolerate those who finance terrorism in the United States," Senate Republican Whip John Cornyn of Texas said in a statement Friday, after the president had vetoed the bill.

Individuals with connections to the Saudi government are alleged to have helped shape the plot to hijack airplanes and destroy key U.S. landmarks like the World Trade Center in New York and the Pentagon. Some say the intention was further revealed in what are known as the 28 pages -- previously classified parts of a congressional investigation into the 9/11 attacks, released earlier this year.

Saudi Arabia has strongly denied any involvement in the attacks.

White House Press Secretary Josh Earnest slammed the veto override after the Senate vote, calling it "the single most embarrassing thing the United States Senate has done, possibly since 1983" in an apparent reference to the last time Congress issued a veto override by such a wide margin.

"You had at least one prominent Republican senator today saying that the members of Senate Judiciary Committee were not quite sure what the bill actually did and to have members of the United States Senate only reasonably informed of the negative impact of this bill on our service members and our diplomats in itself is embarrassing," Earnest said. "For those senators to move forward in overriding the president’s veto that would prevent those negative consequences is an abdication of their basic responsibilities as elected representatives of the American people."

Obama has expressed concerns the bill would possibly damage relations with Saudi Arabia and, also, leave government officials and U.S. citizens vulnerable to lawsuits from other nations.

His top national security officials, including CIA Director John Brennan, have argued that it could also make Saudi Arabia less willing to share crucial intelligence that could disrupt terror plots at home.

"The Saudis provide significant amounts of information that feed into the system that allow us to disrupt these threats," Brennan said Wednesday afternoon. "It would be a absolute shame if this legislation influenced the Saudi willingness to continue to be among our best counter terrorism partners."

ABC News' Ben Siegel contributed to this report.