Senate Minority Leader Mitch McConnell, R-Ky., told CNBC the GOP could make additional offers after Thursday’s proposal.

“We’re going to keep talking, and I understand the president is willing to keep talking,” he told “Squawk on the Street” on Thursday. “We’d like to get an outcome on a significant infrastructure package.”

To reach a deal, the sides would have to resolve not only a gap in the price tag but also differing visions of how to offset the spending. In their counteroffer, Republicans again rejected Biden’s call to raise corporate taxes, contending they could cover infrastructure costs with funds already allocated by Congress or with transportation user fees.

The White House did not immediately respond to a request to comment on the senators’ offer. Sen. Elizabeth Warren, D-Mass., said it wasn’t “a serious counteroffer.”

“First of all, they don’t have ‘pay-fors’ for this, it’s not real,” the progressive Democrat told MSNBC. “They have this illusory notion of how we’re going to take money that’s already been committed to other places and other spending.”

The GOP proposal does not include Biden administration priorities such as $400 billion for home health care, $100 billion for electric vehicle consumer rebates or spending to upgrade housing and schools.

Republicans and the White House have moved closer to agreement on an infrastructure plan but still need to resolve fundamental issues about the scope of a package and how to pay for it, a GOP senator leading the talks said Thursday. Sen. Shelley Moore Capito said the sides are “inching closer” in negotiations ahead of Memorial Day, the date by which the White House wanted to see progress in bipartisan negotiations.

“We’re still talking. I’m optimistic, we still have a big gap,” the West Virginia Republican told CNBC’s “Squawk Box.” “I think where we’re really falling short is we can’t seem to get the White House to agree on a definition or a scope of infrastructure that matches where we think it is, and that’s physical, core infrastructure.”

“The White House is still bringing their human infrastructure into this package and that’s just a nonstarter for us,” she continued, referring to Biden’s plans to put money into programs including care for elderly and disabled Americans.

It is unclear if the two parties can overcome broad ideological differences over what constitutes infrastructure, and how to pay for improvements to it, to strike a bipartisan deal. If negotiations do not show promise, Democrats will have to decide whether to try to pass an infrastructure bill on their own using special budget rules.

The process would bring its own headaches. Senate Democrats would have to keep all 50 members of their caucus on board and comply with strict rules about what can go into a budget reconciliation bill.

The GOP senators who crafted the offer to Biden mentioned that lawmakers could redirect unused coronavirus relief funds for state and local governments to infrastructure, or implement user fees on transportation like electric vehicles. Those Republican solutions could put Biden in a bind.

The president has promised not to raise taxes on anyone who makes less than $400,000 per year. User fees or an increase to the gas tax would put an extra burden on many Americans whose incomes falls under the threshold.

Republicans have said they do not want to raise taxes to cover the costs of improving transportation, broadband and water systems. Biden has called to hike the corporate tax rate from 21% — the level set by the GOP after it cut taxes in 2017 — to at least 25%.

“We can do this without touching … those tax cuts,” Capito told CNBC.

Capito said she sees the potential for bipartisan agreement on transportation spending. She noted that the Senate’s Environment and Public Works Committee — where she sits as ranking member — advanced a roughly $300 billion surface transportation bill that she thinks could guide a broader infrastructure deal.

In trimming his original $2.3 trillion plan, Biden cut out funding for research and development and supply-chain enhancements. He also reduced proposed spending on broadband, roads and bridges.

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