U.S. President Joe Biden has agreed to a compromise with Democrats to further limit who exactly would get a third stimulus check as part of the federal government's latest proposed $1.9 trillion pandemic relief bill, according to CNN Thursday.

At the same time, the Democrats and the White House stood by progressives and agreed that the Senate version of the stimulus bill would retain the $400 weekly emergency jobless benefits included in the House-passed pandemic proposal.

The move is a major compromise to party moderates as Democrats seek to push forward with quickly passing the proposal. New $1,400 financial aid checks are set to be released once Washington legislators finalize a new COVID-19 relief package.

However, fewer Americans could receive the money. Under the agreement, the Senate legislation would instead stop payments for individuals earning $80,000 and couples earning $160,000, a Democratic official, who described the agreement only on condition of anonymity, said.

That means some people who got the last round of $600 stimulus checks in December would not get anything this time.

Unlike the previous two rounds, adult dependents, which include college students, are expected to be qualified for the payments.

The U.S. House of Representatives passed its version of the proposed bill Saturday, but revisions were expected in the Senate version which is set to be unveiled this week.

"I'd call it a modest change," Howard Gleckman, senior fellow at the Urban-Brookings Tax Policy Center, said. "It's going to affect some people, but it's not going to affect a huge number of people," he said in remarks quoted by CNBC.

The change will impact around 8 million Americans who otherwise would have received payment and could now see no checks, a quick estimate by the Urban-Brookings shows.

Chuck Schumer, Senate Majority Leader, said the Senate deliberation would unfurl soon and predicted, "we will have the votes we need to pass the bill."