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 SchumerTrump claims GOP has a 'big surprise' on healthcare Senate Dems step up protests ahead of ObamaCare repeal vote Senate Dems plan floor protest ahead of ObamaCare repeal vote 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 CornynSenators urge Trump to do right thing with arms sales to Taiwan Cornyn: Key vote to advance health bill likely Wednesday GOP ObamaCare fight faces do-or-die procedural vote 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 GrahamGOP senators want surveillance requests from FBI Russia probe Overnight Cybersecurity: New ransomware attack spreads globally | US pharma giant hit | House intel panel interviews Podesta | US, Kenya deepen cyber partnership Graham gets frustrated in public ‘unmasking’ debate 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 RyanCNN's Kohn, Ben Shapiro in Twitter spat after controversial 'killing spree' Ryan tweet Ryan: 'Prayers are being answered' for Scalise's recovery Rift opens in GOP over budget strategy 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.