How to provide additional relief to jobless workers has become a major partisan tension point in preliminary talks for another COVID-19 aid package.

An expanded federal benefit of $600 per week is set to expire at the end of this month, and Speaker Nancy Pelosi says an extension of unemployment insurance must be part of any new package.

But the Trump administration and Republican lawmakers have opposed continuing a benefit that they say could dissuade laid-off workers from reentering the job world. If benefits were extended through January, about 5 of every 6 recipients would earn more in benefits than they would on the job, the Congressional Budget Office said last month.

“We’d like to see some unemployment reforms,” National Economic Council Director Larry Kudlow told the Fox Business Network on Monday. “We’d like a return-to-work-type bonus of a modest nature. We don’t want to give people disincentives … to work.”

Treasury Secretary Steven Mnuchin said last week the administration is working on a “technical fix” that would “incentivize people to go back to work.” While some form of extended benefits are on the table, he told CNBC, “We will not be doing it in the same way.”

[Republicans discussing coronavirus aid package contours]

Eager to trim the size of any extended benefits, Mnuchin said “you can assume it will be no more than 100 percent” of what workers would earn on the job. In crafting the initial benefit in March, Democrats said they decided to settle on a flat rate of $600 per week because the Labor Department said it was unable to calculate benefits based on each worker’s salary.

Speaking on CNN on Sunday, Pelosi said an extension of unemployment benefits must be part of any new package. “We have to find a compromise because we must extend it,” she said, though Pelosi didn’t specifically insist on the $600 weekly figure in her comments.

Two top Democratic economic officials, former Obama administration Treasury Secretary Timothy Geithner and Jason Furman, who served as Council of Economic Advisers chairman, have recommended a $400 weekly benefit. Furman and Geithner, along with former George W. Bush administration CEA Chairman Glenn Hubbard, have also proposed a “hiring bonus” for those returning to work, similar to what some GOP senators have advocated.

The dispute over how to structure the next round of aid comes as the nation’s unemployment rate remains in double digits, though on the decline, since much of the economy was put on ice in March. The unemployment rate in June was 11.1 percent, down from 13.3 percent in May, according to the Bureau of Labor Statistics. But it was still 7.6 percentage points higher than it was in February, leaving 17.8 million unemployed as of last month.

Kudlow also outlined elements of a future aid package that the White House has pushed for weeks. Those include a payroll tax holiday on workers’ wages and a “capital gains holiday,” which would defer payment of capital gains taxes on new asset purchases, possibly for several years.

Democrats, and even some Republicans, have reacted coolly to the idea of helping workers with a suspension of payroll taxes at a time of mass unemployment. And there seemed little likelihood of Democrats backing a suspension of capital gains taxes that could mostly benefit wealthy investors.

“The Fed has spent trillions of dollars bolstering the stock market,” Pelosi said on CNN. “We think we should spend trillions of dollars bolstering the American middle class.”

While Republicans have been considering setting an overall price tag of about $1 trillion for the next package, Pelosi said flatly, “That’s not enough.” House Democrats in May offered up a nearly $3.5 trillion measure, but the Republican-controlled Senate has no intention of considering it.

Pelosi also called for the next package to contain another round of tax rebate checks “so that we have $6,000 for a family of five.” Kudlow said only that “targeted, directed assistance from direct-mail checks to individuals and families” was a possibility that “hasn’t been decided yet.”

Kudlow said an extension of the so-called Paycheck Protection Program, which offers forgivable loans to small businesses, could be considered. He also said President Donald Trump would be willing to consider additional aid to help reopen public schools. “We all agree kids need to be in school,” he said.

Pelosi, speaking on MSNBC Monday, said schools should not reopen without additional federal resources to ensure student and teacher safety. She pointed out Democrats included $100 billion in their May bill to help schools with reopening costs.”Without the resources, we shouldn’t even be thinking about sending [kids] back to school,” she said.

Lawmakers have been inching toward trying to get a new aid package passed before the August recess, though talks have yet to begin in earnest and Congress is out until next week.

Senate Majority Leader Mitch McConnell said Monday on a visit to Baptist Health in Corbin, Kentucky that he’s been crafting a Republican proposal in his office that will serve as the starting point for discussions in his chamber.

“When my members come back next week we’ll start socializing it with them, begin to discuss it with the Democrats and start the legislative process,” McConnell said. “And I think you can anticipate this coming to a head sometime within the next three weeks, beginning next week.”

Lindsey McPherson and Niels Lesniewski contributed to this report.