On Wednesday, President Joe Biden backed an initiative to limit the pool of stimulus check recipients, a change proposed by moderate Democrats. In this new Biden-backed plan, single filers making over $80,000 per year and couples filing jointly earning over $160,000 per year would be completely cut off from receiving a check, according to multiple outlets including Bloomberg and the Washington Post. The cutoff for heads of households would be $120,000.

Those proposed limits are lower than what’s been approved by the House. On Saturday, House Democrats passed a $1.9 trillion aid package that would send $1,400 stimulus checks to most Americans. The House bill would have checks phase out completely at $100,000 for single filers, and $200,000 for couples filing jointly.

However, importantly, the group of recipients receiving the full $1,400 checks is unchanged. As in the recently passed House legislation, single filers earning $75,000 per year or less would still get the full check, as would couples who earn $150,000 or less.

The White House did not immediately respond to Fortune’s request for comment.

This lower cutoff proposal, if passed, would result in roughly 12 million fewer adults getting stimulus checks, according to the nonpartisan think tank Institute on Taxation and Economic Policy, reported by the Washington Post. In addition, roughly 5 million fewer child dependent checks would be sent.

With this latest move, the White House is trying to appease moderate Democrats, including Sen. Joe Manchin, who have pushed to lower the income thresholds to ensure checks are targeted to households who are in the most financial need. A spokesperson for Sen. Manchin did not respond to Fortune’s request for comment.

Those votes will be key in the Senate, where Democrats hold an incredibly slim majority. The chamber has yet to vote on the bill, and Senate leadership intends to use budget reconciliation to pass the package, which would require only 51 votes. But as Republican senators are expected to remain opposed, Democrats would need to secure every vote—including those of moderate Democrats like Sen. Manchin.

Congress is up against an increasingly tight deadline: Democratic leadership has set a March 14 deadline to get a relief bill on President Biden’s desk to avoid a lapse in several pandemic unemployment benefits.