Democrats and Republicans are still fighting over the definition of infrastructure as the Biden administration appears to be wrapping up negotiations over an infrastructure package they value at $1.7 billion.

Transportation Secretary Pete Buttigieg dismissed Democrats' and Republicans' differences as a "dorm room debate over which policies belong in which category" during an appearance on "Fox News Sunday."

COMPARING REPUBLICANS' $928B INFRASTRUCTURE PLAN TO BIDEN'S: WHAT'S IN EACH PROPOSAL?

"We think of it as infrastructure because infrastructure is the foundation that lets people participate in the economy, and as so many people watching this program know, when you're taking care of a loved one, doing some of those things because you don't have the kind of care structure to look after them, you can't even get a job because you're in this elder care situation because somehow we're one of the only developed countries that doesn't take care of this," Buttigieg said. "That's holding you back, the same way it holds you back if you don't have a road or bridge to get to where you want to go."

Lead Republican negotiator Sen. Shelley Moore Capito, R-W. Va., also appeared on "Fox News Sunday" and took issue with the Biden administration including what she considered to be non-infrastructure items in the Democrats' proposal.

Former South Bend, Ind. Mayor Pete Buttigieg listens as President-elect Joe Biden announces Buttigieg as his nominee for transportation secretary during a news conference at The Queen theater in Wilmington, Del., Wednesday, Dec. 16, 2020. (Kevin Lamarque/Pool via AP).

"The president has $400 billion for the caring economy … great things to talk about, but not part of a core infrastructure package," she said. "We just think we would be better off if we just looked at a core, solid definition that is traditionally thought of as infrastructure."

A group of Republicans countered Biden’s $1.7 trillion offer — down from $2.25 trillion — with a trimmed-down $928 billion plan. Instead of bankrolling the proposal by raising the top corporate tax rate from 21% to 28%, they suggested repurposing unused COVID relief funds. 

The White House left the door open to accepting the GOP infrastructure counteroffer on Thursday but said that figuring out how to pay for the plan was unclear.

Press secretary Jen Psaki said President Biden called Capito to thank her for her proposal and was awaiting more details. Psaki said the plan "provides no substantial new funds" for veterans’ hospitals, clean energy jobs, building modern rail systems, repairing transit systems and removing lead pipes. 

A source familiar with the Biden administration’s thinking told FOX Business that there is not $700 billion in unspent federal relief funds as Republicans have said, and the vast majority has been spent or allocated.

"The president's spokesperson said everything has been allocated, it hasn't gone out the door," Capito told "Fox News Sunday." "We have hundreds of billions of dollars that could be reprogrammed towards something as core as infrastructure, and I think that's what we should be looking at. … It's dollars that were way over-allocated that still have yet to be spent." 

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Capito appeared optimistic that the Biden administration would try to work with Republicans instead of bypass them.

"[The president] expressed to me and to our group numerous times his desire to work with us and to negotiate a package," she said. "We're inching towards one another. I understand there's a deadline here. … It's worth it to show this country we can work together, we can reach compromise for the good of everybody." 

Fox News' Morgan Phillips and Fox Business' Jacqui Heinrich and Jonathan Garber contributed to this report.