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President Biden's team sees his meetings this week with key members of Congress on infrastructure as "crucial to determining the path forward, and whether there is enough of an appetite among Republicans for a deal on his spending priorities," The Washington Post reports. Wednesday's Oval Office summit with the "Big Four" lawmakers — House Speaker Nancy Pelosi (D-Calif), Senate Majority Leader Chuck Schumer (D-N.Y.) and Minority Leader Mitch McConnell (R-Ky.), and House Minority Leader Kevin McCarthy (R-Calif.) — was described as cordial but not obviously productive.

Washington's top leaders sparred over a provision of Biden's bill that would incentivize electric vehicle production, taxes, and the very definition of infrastructure, according to several accounts of the meeting. They agreed on the general need to upgrade U.S. physical infrastructure like road, bridges, airports, and broadband. But McConnell and McCarthy also laid out their "red line" for a package: No new taxes.

"We're not interested in reopening the 2017 tax bill," McConnell said after the meeting. "We both made that clear to the president. That's our red line." McCarthy added, "Raising taxes would be the biggest mistake you could make." Biden's red lines, White House Press Secretary Jen Psaki says, are doing nothing and tax increases on families making less than $400,000 a year.

Pelosi said McConnell considers the 2017 GOP tax cuts for the wealthy "sacrosanct," and "we have a different set of values." The group did discuss other funding mechanisms for an infrastructure package, including stepped up IRS enforcement of tax dodgers, she added. "I would not take anything off the table and I'm not drawing any red lines."

"I want to know what we agree on and let's see if we can get an agreement to kick start this," Biden told MSNBC's Lawrence O'Donnell after the meeting, "then fight over what's left, and see if I can get it done without Republicans if need be."

Biden's Wednesday's meeting with the Big Four followed one-on-one meetings this week with swing-vote moderates Sens. Joe Manchin (D-W.Va.) and Kyrsten Sinema (D-Ariz.). On Thursday, Biden hosts a group of Senate Republicans, led by Sen. Shelley Moore Capito (R-W.Va.). That will give Biden a better sense of the odds of a bipartisan deal, Politico reports, but "the most likely scenario remains weeks more of bipartisan theater, followed by a massive reconciliation bill that the White House sells to moderate Democrats as being simply too big to fail."