(Bloomberg) -- Republican senators say they are on track to deliver their counteroffer Tuesday to the Biden administration on the biggest infrastructure package in recent decades.

“It’s not all ready but it’s getting there,” Senator Shelley Moore Capito of West Virginia, who’s leading the GOP effort, said Monday evening.

Capito, along with a group of other Republican senators, will meet on Tuesday with administration officials including Transportation Secretary Pete Buttigieg and Commerce Secretary Gina Raimondo as the two sides continue negotiations that started last week with President Joe Biden hosting a meeting at the White House.

While the GOP initially proposed a $568 billion, five-year package that was well short of Biden’s $2.25 trillion American Jobs Plan, there are increasing signs the party will back a bigger bill. Senate GOP leader Mitch McConnell has said he could envision a total of as much as $800 billion.

Senator Lindsey Graham of South Carolina went further Monday. “We’re not going to do $2 trillion, but I think we could find an $800 to $900 billion infrastructure package,” he said in a statement.

“This has got to be the meat and potatoes of infrastructure: roads, bridges, and ports, and that’s what we’re trying to push,” Graham said, while noting he would also support building out high-speed internet.

Republicans have opposed the tax increases that Biden has proposed to finance the new spending, but yet to detail how they would pay for their plan. Senator Roy Blunt of Missouri said the GOP is working on “a financing authority where you can really leverage some money into public-private partnerships.”

“We don’t have that number yet, but we’re working hard to get there,” Blunt said.

Some Republican senators have backed the idea, embedded in Biden’s proposal, of strengthening Internal Revenue Service enforcement to bolster tax collection.

“I’m in favor of people paying what they owe,” said Pat Toomey of Pennsylvania, one of the GOP senators that will be in the Tuesday meeting, along with Roger Wicker of Mississippi and Mike Crapo of Idaho. “I think there’s a good case that can be made, we can justify that,” Toomey said Monday, while warning that the IRS ought not to target conservative groups.

Tougher IRS enforcement, in the Biden plan, would include banks reporting account flows to the agency. Senator Chuck Grassley, an Iowa Republican, took issue with that on Monday.

‘Big Can of Worms’

“If the IRS gets its eyeballs on personal bank accounts that’s a big can of worms for the tax collector 2decide who gets audited,” Grassley tweeted. The Biden proposal “is ripe for overreach + imposes more burdens on small biz/family farms,” he also said.

Toomey pitched the idea of re-purposing some of the $350 billion that went to state and local governments in the $1.9 trillion Covid-19 relief bill enacted in March -- likely to be a non-starter for Democrats, who had fought for that funding for months, going back to last year.

House Republicans will offer a surface transportation bill of more than $400 billion this week according to a person familiar with the matter. That compares to a $330 billion draft plan offered in the last Congress

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