▶ Watch Video: Biden facing self-imposed deadlines on police reform and infrastructure

Republican senators will announce a new counteroffer on infrastructure on Thursday, after the White House last week unveiled a slimmed-down alternative to President Biden’s original massive proposal. The new offer will be close to $1 trillion, the minimum amount that Mr. Biden has said he will accept for an infrastructure bill, and proposes to be paid for by repurposing unused funds from previously approved coronavirus relief measures.

Senator Roger Wicker, a Republican from Mississippi, told reporters that after a meeting between the chief Republican senators negotiating a counteroffer, the bill would be close to the president’s request, and would cover eight years. He also said that it would not affect the 2017 tax cuts bill signed by former President Trump, which lowered the corporate tax rate to 21%. Mr. Biden has proposed paying for a large infrastructure bill by raising the corporate tax rate to 28%, which is unilaterally opposed by Republicans.

“We’re going to hit a figure very close to what the president said he would accept, and it will end up being the most substantial infrastructure bill ever enacted by the federal government. And if the president gets to make the decision, he will accept it,” Wicker said, alluding to accusations from some Republicans that Mr. Biden’s staff was less willing to negotiate than the president himself.

Wicker said there would be “hardly anything on user fees” to pay for the bill, a method for covering the cost which Mr. Biden has largely rejected. The president has promised he would not raise taxes for any American making under $400,000 per year.

“This is going to be a very good offer, and it moves in his direction,” Wicker said.

Senator Shelley Moore Capito, a Republican from West Virginia who has spearheaded infrastructure negotiations, told reporters that the new offer would be unveiled on Thursday morning. The Republicans had previously proposed a counteroffer of $568 billion, which many Democrats have dismissed as too small.

The White House proposed a $1.7 trillion counteroffer on infrastructure to Senate Republicans last week, roughly half a billion dollars less than Mr. Biden’s initial $2.3 trillion proposal. But Republicans expressed concern that the new offer still included provisions that they did not consider to be related to “traditional” infrastructure needs. Mr. Biden’s new proposal still included provisions on construction of veterans hospitals and on strengthening home care.

“I think we were all a little disappointed that the human infrastructure aspects of the President’s jobs act was still in there,” Capito said. She said she felt Republican senators and Mr. Biden had come to a mutual understanding on the definition of infrastructure during their meeting at the White House earlier this month. 

But Capito also indicated she may seek meet with the president again, saying that the negotiators had been “pretty optimistic” after their previous meeting.

“Maybe that’s a strategy, that we will talk with the president again if he would want to,” Capito said, although she added that Mr. Biden’s staff “has been very open.”

Meanwhile, some Democrats are frustrated at the willingness of the White House to make concessions to Republicans. Progressives could rebel if the White House settles on a narrow package that focuses “traditional” infrastructure projects such as roads, bridges and highways. With the slimmest of majorities in both houses of Congress, Mr. Biden cannot afford to lose any support from his party.

Mr. Biden has also proposed a $1.8-trillion American Families Plan, which is focused on “human” infrastructure, with provisions on health care, child care and education. This proposal has also been met with skepticism by Republicans.