▶ Watch Video: Biden meets with lawmakers to discuss infrastructure plan 

Several moderate Senate Republicans are discussing a potential counteroffer to President Biden’s $2 trillion infrastructure proposal, which they consider to be too big and containing too many provisions unrelated to traditional infrastructure projects, such as highways, bridges and trains.

But Mr. Biden seems unwilling to lower his ambitions and has argued that the modern definition of infrastructure should include things like child care and electric vehicles. The president also appears set on raising the corporate tax rate to pay for his infrastructure bill, which has been met with stiff resistance by Republicans.

Senator Shelley Moore Capito, a Republican from West Virginia, said in an interview with CNBC on Wednesday that the “sweet spot” for an infrastructure proposal would be between $600 and $800 billion and would focus on “roads, bridges, ports, airports including broadband into that, [and] water infrastructure.”

Senator Bill Cassidy, of Louisiana, told reporters on Wednesday that Republicans were working with a bipartisan group including Republican Governor Larry Hogan of Maryland, the president of the National Governors Association, and other members of Congress.

“I think we’ll have a proposal,” Cassidy said.

Nebraska Senator Deb Fischer told reporters that she was working with Capito “trying to put together truly an infrastructure bill.”

“The American people want us to be able to work together on this. They know the needs that are out there, when we talk about traditional infrastructure they want to see us get something done,” Fischer said. “I think everybody in here wants to work in a bipartisan manner, but we have to be realistic. You can’t change the definitions on what infrastructure is just because you have a policy wish list and I think that’s what we’re seeing on the other side.”

Utah Senator Mitt Romney said that the group of Republicans was still in the “early stages” of forming a proposal. He told reporters that Capito’s number was “a little high,” but said “there may be some elements in that that I’m not familiar with.”

“Broadband will be part of that, water, sewer, as well as roads, airports and so forth,” Romney said.

Capito also said in the CNBC interview that she was concerned about the outcome of meetings with the president. A bipartisan group of lawmakers met with Mr. Biden at the White House earlier this week.

“I wouldn’t be being fully forthright here if I didn’t say that’s my concern, that it is going to be a sort of march of folks going to the White House, and we’re doing bipartisan work in our committees, and in the end it becomes a partisan instrument,” she said.

With Republicans firm in their opposition to Mr. Biden’s proposal, Democrats may have to employ budget reconciliation to pass the bill. Most legislation requires 60 votes to advance in the Senate, and Democrats hold a 50-seat majority. Reconciliation allows for budget-related items to pass with a simple majority, although it is a complicated and arduous process. Congress used reconciliation to pass Mr. Biden’s $1.9 trillion American Rescue Plan last month.

GOP Senator Lisa Murkowski said Wednesday that if Republicans are so opposed to Mr. Biden’s plan, they need to come up with an alternative, as well as a way to pay for it.

“I would hope that, as a conference, we can recognize that we should be for an infrastructure package. It’s how we define it, how we pay for it that gets everybody all twisted sideways,” Murkowski said.