The Senate on Tuesday approved legislation that would allow victims of the 9/11 terror attacks to sue Saudi Arabia, defying vocal opposition from the White House. 

The upper chamber approved the Justice Against Sponsors of Terrorism Act by unanimous consent.

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"This bill is very near and dear to my heart as a New Yorker because it would allow the victims of 9/11 to pursue some small measure of justice," Sen. Charles SchumerCharles (Chuck) Ellis SchumerThe Hill's 12:30 Report — Sponsored by Delta Air Lines — GOP centrists in striking distance of immigration vote Schumer: Trump should take Kim Jong Un off 'trip coin' Overnight Finance: Trump signs repeal of auto-loan policy | Justices uphold contracts that bar employee class-action suits | US, China trade war 'on hold' MORE (D-N.Y.) said. "[This is] another example of the [John] Cornyn-Schumer collaboration, which works pretty well around here." 

President Obama has threatened to veto the bill. Schumer said he wouldn’t uphold a veto, and expects that most senators wouldn't, either.

"I think we easily get the two-thirds override if the president should veto," Schumer said.

Sen. John CornynJohn CornynHillicon Valley: Experts worry North Korea will retaliate with hacks over summit | FBI works to disrupt Russian botnet | Trump officials look to quell anger over ZTE | Obama makes case for tighter regs on tech Senate GOP sounds alarm over Trump's floated auto tariffs Administration works to assuage critics over ZTE deal MORE (R-Texas) said he and Schumer are talking with leadership in both parties to get an "expedited" vote on the bill in the House.

White House press secretary Josh Earnest reiterated Obama's opposition to the bill on Tuesday.

“Given the concerns we have expressed, it’s difficult to imagine the president signing this legislation,” Earnest said. 

The bill would allow victims of terror attacks on U.S. soil or surviving family members to bring lawsuits against nation-states for activities supporting terrorism. 

Despite bipartisan support for the legislation, it hit a snag last month when Sen. Lindsey GrahamLindsey Olin GrahamHouse GOP sets three FBI interviews in Clinton probe Trump on collision course with Congress on ZTE The Hill's 12:30 Report — Sponsored by Delta Air Lines — GOP centrists in striking distance of immigration vote MORE (R-S.C.) said he was blocking the legislation over concerns it would open up the U.S. to lawsuits from foreigners accusing Washington of supporting terrorism. 

But Graham's office said he dropped his hold over the recent recess. Cornyn thanked Graham and other GOP senators for "their willingness to work with us to deal with their concerns." 

The legislation will now head to the House, where lawmakers have also introduced their own version of the bill.

Speaker Paul RyanPaul Davis RyanThree House Dems say they'll oppose immigration floor vote over possible wall funding Dems after briefing: 'No evidence' spy placed in Trump campaign Senate approves new sexual harassment policy for Congress MORE (R-Wis.) has voiced skepticism about the legislation.

"I think we need to look at it," Ryan told reporters last month. "I think we need to review it to make sure we are not making mistakes with our allies and we're not catching people in this that shouldn't be caught up in this." 

The comments created a rare area of agreement between GOP lawmakers and the White House, which struggled to convince Democrats that the legislation could undermine national security. 

Earnest told reporters last month that he was "gratified" by Ryan's comments.

The legislation has also drawn criticism from the Saudi government. Top Saudi officials reportedly threatened to sell off billions of dollars in U.S. assets if Congress passed the bill.

Saudi Arabia's foreign minister, Adel al-Jubeir, pushed back against the reports in Geneva earlier this month while warning that the legislation could impact Saudi investments, according to Reuters. 

The senators pressed back against criticism that the legislation targets Saudi Arabia, noting that the legislation only allows a lawsuit.

"Look, if the Saudis did not participate in this terrorism, they have nothing to fear about going to court," Schumer said. "If they did, they should be held accountable."

Cornyn called the potential that Saudi Arabia could sell U.S. assets a "hollow threat," saying, "they're not going to suffer a huge financial loss in order to make a point."

Updated at 2:36 p.m. Jordan Fabian contributed.