When President Obama vetoed a bill that would allow 9/11 victims’ families to file lawsuits against Saudi Arabia for its alleged role in the attacks, he set the stage for the first-ever override of a veto in his presidency.

Fifteen years after 9/11, the victims’ families continue to wield extraordinary political influence in Washington, and their lobbying and pressure in recent weeks is why the bill is still likely to become the law of the land despite Obama’s veto.

“We are outraged and dismayed at the President’s veto of JASTA and the unconvincing and unsupportable reasons that he offers as explanation,” the group 9/11 Families & Survivors United for Justice Against Terrorism, which has been a leading proponent of the bill, said in a statement.

In a statement accompanying his veto Friday, Obama said the Justice Against Sponsors of Terrorism Act, known more commonly by its acronym, would compel foreign governments to file suits against the United States and would “create complications in our relationships with even our closest partners.” Obama noted that “a number of our allies and partners have already contacted us with serious concerns about the bill.”

Opponents say the bill undermines the bedrock foreign policy principle of sovereign immunity and would unleash a torrent of foreign lawsuits against the United States, including potentially for drone strikes that have killed innocent civilians.

But supporters have long debated those assertions and insist that JASTA would not bring about the grave consequences that Obama and other opponents of the legislation imagine.

“No matter how much the Saudi lobbying and propaganda machine may argue otherwise, JASTA is a narrowly drawn statute that restores longstanding legal principles that have enjoyed bipartisan support for decades,” the family group said. “It will deter terrorism and hold accountable those nations that support and fund it.”

Three sources close to the legislative proceedings told The Daily Beast that the Senate is likely to take an override vote on Tuesday, or Wednesday at the latest. And the math appears to be in favor of the bill’s backers there and in the House of Representatives.

“I'm confident our members of Congress will remain steadfast, vote for the override, and enact JASTA,” Terry Strada, the chair of the family group, told The Daily Beast. Strada’s husband, Tom, was killed in the attack on the World Trade Center.

“This is a disappointing decision that will be swiftly and soundly overturned in Congress,” Chuck Schumer, the senior senator from New York and the likely next Democratic leader, said in a statement. “I believe both parties will come together next week to make JASTA the law of the land.”

Some senators had mounted an effort to try and change the language of the bill in order to satisfy 9/11 families and the administration. But if there was ever any hope of compromise, it appears to have passed.

In recent weeks, Sens. Lindsey Graham and Bob Corker tried to craft some alternative and were met with condemnation by the 9/11 families, who accused the lawmakers of trying to delay the Senate vote to overturn the veto.

A former U.S. national security official, speaking on condition of anonymity given the sensitivity of the issues, said Congress missed an opportunity months ago to have a fuller debate on the bill, noting that JASTA was never the subject of hearings, as is often the case for important or controversial legislation.

“This is the problem when Congress doesn’t do the hard work on the front end. It makes it even harder to do your job on the back end,” the former official told The Daily Beast.

Lawmakers could have explored alternative arrangements, such as paying further compensation to the family members, the former official said. But ultimately, not enough lawmakers appear willing to be seen as siding with Saudi Arabia over the victims, even if they oppose the legislation on principle.

Under U.S. law, Americans can sue foreign governments for acts of terrorism that occur overseas. JASTA would allow lawsuits to go forward if the attack occurred in the U.S., effectively ending sovereign immunity when it comes to terror attacks.

If that happens, the bill’s opponents warn, trial lawyers will make billions on lawsuits against governments and corporations that are alleged to have played some role in supporting terrorism.

And that, they warn, will trigger reciprocal litigation, potentially leading to the freezing of U.S. companies’ assets or charges against government employees, diplomats, or military personnel.

The European Union delegation to the United States warned of as much in a démarche to the State Department earlier this week: “State immunity is a central pillar of the international legal order. Any derogation from the principle of immunity bears the inherent danger of causing reciprocal action by other states and an erosion of the principal as such.” The European Union also warned that if the U.S. enacts the law, other countries are likely to put in place their own parallel legislation “leading to a further weakening of the principles of State sovereign immunity.”

The bill is opposed by lawmakers and government officials in an array of countries, including the United Kingdom, France, Jordan, Pakistan, the Netherlands, the United Arab Emirates, Morocco, Bangladesh, Qatar, Bahrain, Kuwait, and Sudan. And many of those countries, like France and the United Kingdom, face no imminent threat of lawsuit in a U.S. federal court.

Companies that do business in Saudi Arabia and elsewhere in the Middle East also lobbied congressional leaders to withdraw their support for JASTA.

The chairman and CEO of the Dow Chemical Co., Andrew Leveris, wrote personally to House Speaker Paul Ryan urging him to “reconsider” his support of the bill and noting that Dow was “establishing partnerships that address the fundamental causes of radicalism,” particularly in Saudi Arabia.

And the chairman and CEO of GE, Jeffrey Immelt, wrote to Senate Majority Leader Mitch McConnell that enactment of the bill would jeopardize U.S. relations with Middle Eastern countries at an especially precarious time. “Our government’s actions have often confused our partners and they don’t know whom to trust,” Immelt wrote. “This bill is the wrong action at the wrong place at the wrong time. I truly believe we will regret this move.”

Proponents of the bill say it will not wreck the system of sovereign immunity because existing laws and treaties will prevent the kinds of lawsuits that critics fear. The backers have accused opponents of caving to pressure from U.S. lobbyists hired by Saudi Arabia, the same ones they say worked to keep 28 pages of a congressional investigation about suspected Saudi involvement in the 9/11 attacks from public view. Those pages were finally released, with partial redactions, in July.

The advocacy group 9/11 Families & Survivors United for Justice Against Terrorism fingered Corker and Graham in particular as being influenced by Saudi pressure.

“Both Senators Corker and Graham studied the bill earlier this year—delaying its Senate passage—and made changes to the bill’s text for many of the same concerns they are now raising,” the group said in a statement. The Senate passed JASTA in May, and the House followed suit earlier this month.

“If they had lingering concerns at that time, they never voiced them when the Senate unanimously passed the bill,” the families group said. “Not until the Saudi lobbyists came knocking.”

Saudi Arabia and its American lobbyists have mounted a concerted campaign against passage of the bill.

Saudi Arabia has threatened to liquidate $750 billion in Treasury securities and other assets should the bill pass. But it’s unclear how the Saudis would unload such an enormous sum without losing much of their investment in a fire sale and setting off a global panic.

But those threats and Saudi Arabia’s insistence that it has helped the United States conduct vital counterterrorism operations appear not to be enough to persuade lawmakers to let the bill die.

In vetoing JASTA, Obama found himself in a dilemma with little political upside. Defying the families of the 9/11 victims was sure to inspire their outrage. But had he allowed the bill to become law, he would have been seen as turning his back on the U.S. intelligence community and the military.

On Thursday, Secretary of Defense Ash Carter testified before the Senate Armed Services Committee that the law could jeopardize U.S. forces overseas. And earlier this year, officials told The Daily Beast that the law would alienate one of United States’ most important partners in fighting terrorist networks. Within military and intelligence circles, there’s an awareness that the U.S.-Saudi relationship is far from perfect, but there’s also a belief that the bill’s proponents are putting the blame for 9/11 in the wrong place.

“As far as I am concerned, Osama bin Laden attacked the United States,” one official said at the time.

And yet officials have sometimes been at pains to explain precisely how the law would adversely affect U.S. troops or intelligence officers. Both Carter and Marine Gen. Joseph Dunford, the chairman of the Joint Chiefs of Staff, who also testified this week, seemed reticent to dive into the discussion of the bill.

“We are not the ones dealing with it, nor am I, at least, an expert on it,” Carter said.

“[W]ere another country to behave reciprocally, this could be a problem for our service members, and this is something that, at the Department of Defense, we are concerned about.”

Dunford said there would be “second-order effects,” without specifying what those would be.