A House-passed bill that would extend a financial lifeline to thousands of victims suffering health problems from the 9/11 terrorist attacks is facing some political resistance in the Senate.

Utah Republican Mike Lee has a hold on the legislation, according to the nation’s top firefighters union. And Kentucky Republican Rand Paul objected Wednesday when New York Democrat Kirsten Gillibrand sought unanimous consent to bring up the bill for a vote.

[9/11 aid bill passes House after emotional lobbying campaign]

Both Lee and Paul are fiscal hawks who often oppose new spending unless paid for with cuts elsewhere in the federal budget.

“Any new program that will have the longevity of 70, 80 years should be offset by cutting spending that’s less valuable,” Paul said. “We need at the very least to have this debate. I will be offering up an amendment if the bill should come to the floor, but until then I will object.”

The measure would effectively make permanent a special compensation fund for first-responders and other victims of the 2001 attacks, while providing however much money is needed to pay all eligible claims. It passed the House on an overwhelming 402-12 vote Friday, despite a cost estimate from the Congressional Budget Office that it would require about $10.2 billion in the first decade, and more in the decades beyond.

“Our nation has a moral obligation to act quickly to ensure injured and sick responders receive the compensation they need and deserve for losses sustained in service to their country, just as they acted quickly when we needed them on 9/11,” Harold Schaitberger, general president of the International Association of Fire Fighters, wrote to Lee in a letter Wednesday.

A Lee aide didn’t dispute the hold, but suggested it would not actually stop the bill. “Sen. Lee fully expects the 9/11 compensation bill to pass before the August recess,” the aide said.

House Judiciary ranking member Doug Collins said during floor debate that the cost of the measure was a concern. The Georgia Republican also said it was unlikely to clear the Senate for President Donald Trump’s signature without offsets. Lee’s staff didn’t detail what his specific objections are, but the Utah Republican has been a hawk on spending issues throughout his tenure in the Senate.

Senate Majority Leader Mitch McConnell said after the House vote last week that he planned to bring up the bill for a Senate vote “soon.” A spokesman for the Kentucky Republican confirmed Wednesday that the plan is to vote on the measure before the August recess.

Gillibrand, a Democratic presidential hopeful, pushed for an immediate vote Wednesday, expressing impatience with GOP leadership.

“These first-responders, many of them sick and dying, had to come back again and again and again and walk these halls,” she said, referring to each time the compensation fund had to be extended. “Once again, first-responders are being forced to come here and knock on office doors.”

Her own bill to extend the fund has 73 co-sponsors, Gillibrand said on the floor. “In these divided times, what other bill can you imagine could have so much support in both parties?” she asked.

The White House hasn’t taken an official position on the House-passed measure. There are likely veto-proof majorities in both chambers given the lopsided House vote and the number of Senate backers.

Speaking at a Wednesday afternoon press conference, Senate Minority Leader Charles E. Schumer downplayed the notion of attaching the 9/11 bill to some other must-pass vehicle, like an emerging debt limit and spending caps deal. 

“We don’t need it attached to anything else,” the New York Democrat said. “That’s how fumbles occur. That’s how bills don’t get passed.”

Still, Schumer acknowledged the possibility that the legislation could get mixed up with a larger package, though it hasn’t been part of his negotiations with Treasury Secretary Steven Mnuchin and Speaker Nancy Pelosi.

“I’ve heard a rumor that it would be on the debt ceiling,” he said. “Maybe there will be good faith to do it another way, but you never know what happens.”