WASHINGTON, D.C. — A group of Senate Republicans plans to present their latest offer to the White House on a major new infrastructure package on Thursday, with one member saying it will weigh in at almost $1 trillion.

“This is going to be a very good offer,” Sen. Roger Wicker of Mississippi told reporters Tuesday. The latest counter will be “close” to $1 trillion, spread over eight years, he said.

Democratic lawmakers have warned that time is running short to determine whether a bipartisan deal on infrastructure is possible, with progressives already calling for a go-it-alone approach using fast-track budget procedures. A new offer around $1 trillion would still be well short of Friday’s $1.7 trillion proposal from the White House.

West Virginia Sen. Shelley Moore Capito, the lead Republican negotiator, said the group might request a meeting with Biden, since he seemed more open to a deal in a gathering last Thursday than his staff later did. Wicker similarly said that if Biden is able to decide on a response to the new GOP plan, rather than administration staff, the president would accept it.

“We were pretty universal on this, I mean there was no dispute with what he said to us in the room that day,” Capito said, underscoring the GOP view that Biden had indicated he could accept a $1 trillion bill. “That’s why I think, when we left there, we were pretty optimistic that this is doable.”

White House press secretary Jen Psaki pushed back against that characterization in a briefing Tuesday.

Friday’s $1.7 trillion plan was “approved by the president, was signed off by the president, every single detail of that was directed by the president of the United States. He does not take a hands-off approach to legislating, negotiating and determining what kind of counterproposals we should put forward,” Psaki said.

“This is an ongoing negotiation, we’re eager to see” the forthcoming GOP offer, she said.

Wicker said the new GOP counterproposal will be able to resolve the talks before Memorial Day — May 31 — in line with Biden’s goals.

On Friday, the Biden administration reduced its proposal by more than $500 billion from an initial $2.25 trillion by lowering spending on roads, bridges and broadband and saying he is willing to make investments in the manufacturing sector in separate bills — like the China-focused legislation on the Senate floor this week.

The two sides have been defining the size of the package differently, with Republicans including money already expected to be in the spending pipeline. The GOP senators characterized their initial offer as $568 billion.

Wicker said the Republican plan would largely be paid for by repurposing Covid relief money for state governments that was authorized by the $1.9 trillion pandemic-relief bill enacted in March. Additionally, he indicated the GOP offer would count the money spent in the China bill toward the total.

That may be a non-starter for the White House, however, which has proposed corporate tax increases to pay for its plan.

Psaki said that, apart from the main infrastructure talks, there are encouraging moves in Congress this week.

On Wednesday, the Senate Energy and Public Works Committee plans to vote on a bipartisan surface transportation bill.

“That’s a $303 billion infrastructure bill that is a great down payment,” Psaki said. “It’s very much aligned with the president’s proposal and initiatives.”

The Senate is also working on a bipartisan bill, known as the Endless Frontier Act, to ramp up research spending in an effort to strengthen competition against China, which has become a broader vehicle for spending items including money for semiconductors.

“We expect the Senate to finalize an agreement on the innovation and competition act this week,” Psaki said. “I’d say that’s progress.”