Senate Majority Leader John Thune said Republicans are exploring whether parts of the SAVE America Act could be advanced through the budget reconciliation process, a strategy he suggested may have been what late Sen. Lindsey Graham discussed with President Donald Trump before his death.

Speaking in an interview with The New York Post, the South Dakota Republican said he believes Graham, who chaired the Senate Budget Committee, may have been referring to reconciliation when he told Trump the GOP was "all set" on the SAVE America Act during what Trump has said was their final phone conversation.

Trump revealed the conversation during an appearance Sunday on NBC's "Meet the Press," saying Graham told him, "We're all set for the SAVE America Act," but he did not elaborate.

The SAVE America Act, Trump's top legislative priority this year, would require proof of U.S. citizenship to register to vote in federal elections and include other election-related reforms. Republicans have repeatedly failed to advance the measure in the Senate because Democrats have blocked it with the filibuster.

"Perhaps what Lindsey was talking to the president about, I don't know this for a fact, was whether or not there was an option for reconciliation, and there is a way in which I think you could," Thune said.

Thune stressed that Republicans are nowhere near the 60 votes needed to overcome a Democrat filibuster and have no realistic path to winning Democrat support for the legislation.

Instead, he said Republicans are examining whether portions of the measure could qualify under Senate budget reconciliation rules, which allow certain fiscal legislation to pass with a simple majority.

"It's got to be principally budgetary, not policy-oriented. And if the budgetary impact is incidental to the policy impact, then it's usually ruled a violation," Thune said, referring to Senate rules enforced by the parliamentarian. "I'm not denying there's some level of subjectivity."

He pointed to one proposal that could potentially qualify by tying election measures to federal spending.

"Figuring out a way to incentivize states to pass or to implement photo ID in their states through financial incentives is something that's been talked about as a possible reconciliation option," Thune said. "How you design or structure it matters a lot."

Graham, who died Saturday night after what was described as a brief and sudden illness, had been closely involved in reconciliation planning as chair of the Senate Budget Committee.

Republicans have previously used reconciliation to bypass the Senate filibuster for budget-related legislation. However, measures must have a primary budgetary impact to comply with Senate rules.

On Wednesday, the House Budget Committee unveiled a budget resolution that would begin the reconciliation process for a $95 billion package that includes $60 billion for defense, $13 billion for intelligence, $12 billion in farm aid, and $10 billion in grants aimed at advancing elements of the SAVE America Act.