Updated May 13, 2021 at 4:43 PM ET

President Biden continued conversations with congressional Republicans on Thursday in the hopes of landing a bipartisan deal on an infrastructure package, but major hurdles persist over what items would be in the measure, and how it might be paid for.

Biden has pitched a roughly $2 trillion infrastructure plan, in addition to another massive spending proposal on families and education.

Following Thursday's meeting, Biden said the conversation had not yet led to any concrete compromises, but that he had outlined to the Republican leadership his ambitions for the package's scope and source of funding. Biden said the two camps agreed that Republicans would return with a counter offer and that discussions on the matter would continue next week.

"I am very optimistic that we can reach a reasonable agreement, but even if we don't, it's been a good faith effort that we started," Biden told reporters following an unrelated press conference on the CDC's updated coronavirus guidance.

Shortly before the meeting, Biden made a point to say he was open to compromising across the aisle to reach a deal.

"I know they're sincere about it and so am I," Biden told reporters. "I assure you this is in good faith, it's a genuine effort. I think we can get there."

Biden met with several Senate Republicans Thursday, including West Virginia's Shelley Moore Capito, who's leading GOP negotiations on infrastructure.

On Wednesday Biden hosted the four top Senate and House leaders in the Oval Office in an effort to jumpstart discussions on steering an infrastructure measure through Congress.

After that discussion, however, Republican Senate leader Mitch McConnell and GOP House leader Kevin McCarthy made clear that there are a few key points on which they are unwilling to concede or compromise.

"Senate Republicans are not interested in revisiting the 2017 tax bill. I think the president and vice president understand that," McConnell told reporters after the meeting, referring to the 2017 tax cuts that Republicans passed on Capitol Hill and former President Donald Trump signed into law.

To pay for his infrastructure measure, Biden has proposed raising corporate taxes, and to pay for his families plan, he's seeking to impose higher taxes on the richest Americans, who he says have gone far too long without paying their fair share. Biden's proposed changes would pare back many of the Trump tax cuts.

Also at issue is exactly what should qualify as "infrastructure" under any potential funding agreement. Republicans want to keep a narrow scope, limiting spending to physical projects like roads and bridges, while Democrats also hope to allocate hefty sums to clean energy and to social issues like home- or community-based care for the elderly and people with disabilities.

"I think there's a place that we can find bipartisanship," McCarthy told reporters. "One thing I brought up to the president: We first have to start with a definition of what is infrastructure. That's not home health. That's roads, bridges, highways, airports, broadband. Those are the places we could find common ground to work together."

McCarthy also referenced a Wednesday report from the Department of Labor that showed a 4.2% increase in consumer prices — the largest year-over-year rise since a 4.9% spike in the fall of 2008.

It's unclear whether the increase is a short-term jump, or a longer-term rise.

"You won't find any Republican who's going to go raise taxes, I think that's the worst thing you can do in this economy," McCarthy said. "You're watching food costs go up, you're watching housing costs, lumber costs."

Democrats have sought to find some common ground with Republicans on their spending plans, despite holding a majority — albeit razor thin — in both chambers of Congress.

But Biden, in a Wednesday interview with MSNBC's Lawrence O'Donnell, reiterated that he would be willing to move forward without the support of Republicans if the two parties are unable to strike a deal in a timely manner.

He also indicated he'd be open to splitting the efforts into two.

"I want to get a bipartisan deal on as much as we can get a bipartisan deal on," he told O'Donnell. "And that means roads, bridges, broadband, all infrastructure. But I'm not giving up on the fact that we have, you know, 2 million women who are not able to go back to work because all the daycare centers are closed. They're out of business. And so, they can't go back to work."

He added: "Let's see if we can get an agreement to kickstart this — and then fight over what's left and see if I can get it done without Republicans, if need be."

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