On Thursday, a bipartisan group of senators added to the debate by introducing an amendment that would prohibit “upper-income taxpayers” from being able to receive $1,400 stimulus checks. The lawmakers did not include specific monetary figures for the cut-off.

First reported by Politico, the amendment to the Senate’s budget resolution—which will allow Democrats to pass much of Biden’s $1.9 trillion COVID relief package without any Republican support—was led by senators Joe Manchin (D-W.Va.) and Susan Collins (R-Maine).

The measure’s purpose is to “establish a deficit-neutral reserve fund relating to targeting economic impact payments to Americans who are suffering from the effects of COVID–19, including provisions to ensure upper-income taxpayers are not eligible.”

Along with Manchin and Collins, the amendment is supported by Bill Cassidy (R-La.), Shelley Moore Capito (R-W.Va.), Maggie Hassan (D-N.H.), John Hickenlooper (D-Colo.), Mark Kelly (D-Ariz.), Angus King (I-Maine), Rob Portman (R-Ohio), Mitt Romney (R-Utah), Mike Rounds (R-S.D.), Jeanne Shaheen (D-N.H.), Kyrsten Sinema (D-Ariz.), Jon Tester (D-Mont.), Thom Tillis (R-N.C.), and Mark Warner (D-Va.).

The Senate is expected to pass the budget resolution by the end of this week, but first the chamber has to get through Thursday’s “vote-a-rama”—a marathon session where lawmakers will be tested on their support for a variety of issues.

Biden has reportedly expressed willingness to negotiate who can receive the stimulus payments. According to the New York Times, Biden told House Democrats on a caucus call Wednesday that “we can better target the number. I’m okay with that.”

“We can’t walk away from an additional $1,400 in direct checks, because people need it,” he said. “I’m not going to start my administration by breaking a promise to people.”

Under previous COVID-19 legislation, stimulus checks have gone to individuals with up to $75,000 in income and couples earning up to $150,000. But some lawmakers and economists have argued the income thresholds have been too broad and that the next round should go to Americans hit hardest by the pandemic.

Manchin, a critical vote in relief negotiations as a moderate Democrat in the 50-50 Senate, has expressed support for lowering the thresholds for stimulus check eligibility to $50,000 for individuals and $100,000 for joint filers.

“They’re trying to make sure it’s targeted to the people who really need it,” Manchin told CBS News earlier this week. “That’s what will happen and it will go out quickly once we get this passed.”

Newsweek has reached out to Collins and Manchin’s offices for further comment on the budget amendment.