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

The private meeting was billed as more of a conversation with West Virginia GOP Sen. Shelley Moore Capito, rather than a formal negotiation, the White House said. 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,” and agreed to reconnect again Friday, according to a White House official granted anonymity to discuss the private talks.

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,” said White House Press Secretary Jen Psaki 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 to pay for it. Instead, Biden wants to hike the corporate tax rate to generate revenue for his $1.7 trillion package, a nonstarter for Senate Republicans.

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 a party-line votes. The Senate parliamentarian signaled new procedural 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 ruling, the parliamentarian said only one package would be available this calendar year.

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 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 $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 in the narrowly divided Congress where the administration has few votes to spare if the president tries to push the package to passage under the budget rules that allow for a majority vote.

Psaki downplayed the 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. In remarks in Oklahoma, he noted those 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 broach the divide to hash out issues.

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