"It's difficult to imagine the president signing this legislation. That continues to be true," White House press secretary Josh Earnest said in May.
At its core, the back and forth over the measure centres on the belief, held by a number of 9/11 families and a bipartisan group of politicians, that Saudi Arabia was involved in the September 11 attacks - 15 of the 19 terrorists were Saudi.
Democrat Senator Chuck Schumer, a co-sponsor of the bill, told reporters in May that he is confident that if the bill is vetoed the Senate would be able to override it because they do not believe the White House arguments stand up.
"I'm pleased the House has taken this huge step forward towards justice for the families of the victims of 9/11," Schumer said.
The Saudi Foreign Minister previously said that his country's opposition to the bill was based on basic principles of sovereign immunity.