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(NEXSTAR) – The Biden Administration is stopping short of shooting down hopes of a fourth stimulus check, but signaled Thursday that the president is focused on “putting people back to work” rather than short-term relief.

During a press briefing Thursday, press secretary Jen Psaki was asked whether the proposed American Jobs and Families Plans would provide enough of an economic boost that a fourth round of checks would be unnecessary.

“He’s happy to hear from a range of ideas on what would be most effective and what’s most important to the economy moving forward,” said Psaki. “But he’s also proposed what he thinks is going to be most effective for the short term for putting people back to work, to getting through this pivotal period of time, and also to making us more competitive over the longterm.”

The comments suggest little movement toward a new batch of payments in recent weeks. Last month, Psaki deferred to congress on a fourth check proposal and said “those are not free.”

The White House has been focused on building support for the president’s $1.7 trillion American Jobs Plan and a separate $1.8 trillion American Families Plan, he has been seeking a bipartisan deal with Republicans for weeks, but may elect to try and push forward with Democratic votes if those talks continue to prove unsuccessful.

Talks over Biden’s top legislative priority have been moving slowly, a daunting undertaking given the massive infrastructure investment, and time for a deal is running out. The administration has set a June 7 deadline to see clear direction and signs of progress.

Privately, the president has sized up the GOP’s latest $928 billion counteroffer as unworkable, in large part because it taps unused COVID-19 funds. Instead, Biden wants to hike the corporate tax rate — a nonstarter for Senate Republicans — to generate revenue for his $1.7 trillion package.

The ongoing talks may take on new importance after Democrats suffered a setback Wednesday in their efforts to attempt to pass this and other Biden priorities on party-line votes. The Senate parliamentarian signaled new limits on how many times Democrats can use the budget reconciliation process that allows a 51-vote threshold, rather than the 60 votes typically needed to advance legislation. In a four-page memo, the parliamentarian made it clear Democrats will likely have only one more opportunity to use the budget process this year, essentially closing the door on a strategy they were eyeing for multiple votes.

Heading into the next round of meetings Friday, Capito was expected to reup the GOP’s push to repurpose the coronavirus relief fund to pay for infrastructure investments, said Senate Republican leader Mitch McConnell, who has tasked Sen. Shelley Moore Capito of West Virginia to lead the discussions.

“That’s the key to getting a bipartisan agreement,” McConnell said at a press conference in Kentucky. He said he particularly wants to halt unemployment assistance that he says is preventing Americans from returning to work.

“The coronavirus is behind us. We need to get back to work,” McConnell said.

The Associated Press Contributed to this report.