WASHINGTON (AP) — For nearly an hour, President Joe Biden and the top Senate Republican negotiating infrastructure met behind closed doors — two seasoned legislators engaged in another round of conversations, but emerging with few outward signs of tangible progress ahead of a deadline next week.

The White House billed the private meeting Wednesday as more of a conversation with West Virginia GOP Sen. Shelley Moore Capito, rather than a formal negotiation. No new offers were expected to be presented. More than anything, the session in the Oval Office was seen through the political lens of the president and Republicans trying to show the public what Americans say they want — a willingness to work together, even if no deal is within reach.

Biden and Capito had a “constructive and frank conversation," according to a White House official granted anonymity to discuss the private talks. The senator's office said she is encouraged by the ongoing conversations. The two agreed to reconnect Friday.

Still, 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.

“The fact that the president is having Sen. Capito here today and has been having ongoing discussions with Republicans in the Senate and that he’s eager to find a path forward on bipartisanship work certainly tells you, I think, what you need to know about what he thinks about working with people even when there’s disagreement,” White House Press Secretary Jen Psaki said ahead of the afternoon session.

Privately, the president has sized up the GOP's latest $928 billion offer 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 more only one more opportunity to use the budget process this year, essentially closing the door on a strategy they were eyeing for multiple votes.

Friday's next round of talks between Biden and the Republican senator would overlap with the release of the May jobs report, as private economists estimate a meaningful increase from the disappointing April figures. May’s jobs figures could provide evidence as to whether Biden’s earlier $1.9 trillion COVID-19 relief package has helped put the country on track to recover the jobs lost to the pandemic.

Heading into the meeting, 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 her 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.

Together, the president and the Republicans both have political incentives to negotiate a bipartisan accord over his sweeping investment package, even if no deal is within sight. For Biden, reaching across the aisle and cutting deals in Congress is central to his brand of politics. Republicans can also score political gains by trying to work with a popular president.

Yet an initial Memorial Day deadline came and went without results, and in the latest round of talks, Biden and a core group of GOP senators appear to have pulled farther apart. Democrats, who hold slim majorities in the House and Senate, are watching warily as the White House and Republicans try to narrow the gap between the president's initial ideas for a massive investment in not just roads and bridges but the “human” infrastructure of hospitals and child and senior care facilities, and a GOP approach that is more focused on traditional infrastructure projects.

The White House has pared back the president’s initial $2.3 trillion bid, now tallied at $1.7 trillion, with Biden proposing to fund the investment by raising the corporate tax rate from 21% to 28%.

Without a bipartisan agreement with Republicans, Biden will be faced with trying to muscle support from Democrats alone. That approach also poses political challenges, particularly in the evenly split Senate, where the administration has no votes to spare if the president tries to push through the package under the budget rules that allow for a simple majority vote.

Psaki downplayed comments Biden had made Tuesday that were seen as critical of two Democrats, presumably Sen. Joe Manchin of West Virginia and Sen. Krysten Sinema of Arizona. Speaking in Tulsa, Oklahoma, he noted Democrats who don't always vote with the party, blaming them for stalling his agenda.

Psaki said the president considers both Manchin and Sinema “good working partners" and pointed to the Capito meeting as an example of his willingness to cross the divide to hash out issues.

Biden's own thinking is that the Republican proposal, while improved from an earlier $568 billion opening bid, is unworkable because the Republicans want to tap unspent COVID-19 funds to pay for the spending.

The president, in meetings with his team, has zeroed in on the questions the GOP proposal raises — namely, which coronavirus relief funds to possibly shelve. Biden’s view is that tapping the COVID-19 funds would unduly burden the middle class, including small business owners, who are receiving aid during the pandemic crisis.

For Republicans, the corporate tax hikes are a red line they will not cross. They instead want to pay for the infrastructure investment with virus aid money as well as gas taxes and other fees on consumers.

Congress is away for a weeklong Memorial Day break, but faces a deadline when lawmakers return next week.

The White House said the president is also eyeing action in the House next week, when the Transportation and Infrastructure Committee is set to begin debating a big highway reauthorization bill that is being closely watched as a potential building block toward the broader package.

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Associated Press writers Alan Fram, Darlene Superville and Josh Boak contributed to this report.