WASHINGTON (News Nation) — Unemployment assistance, eviction protections and other relief for millions of Americans are at stake as White House officials launch negotiations with House Speaker Nancy Pelosi on a new coronavirus aid package in Congress ahead of looming deadlines.

While Senate Republicans had challenges rolling out their own $1 trillion counter proposal, the White House, Senate and Congress resume their efforts to agree on a new economic aid package.

Aid runs out Friday for a $600 weekly jobless benefit on top of state unemployment funds for out-of-work Americans. Republicans want to cut it to $200 a week, saying that the federal bump is discouraging employees from returning to work.

With the virus death toll rising and nearly 4.3 million infections nationwide, according to Johns Hopkins University, both parties are eager for a deal. There is general agreement that more money is needed for virus testing, to help schools prepare to open in the fall and to shore up small businesses.

Treasury Secretary Steven Mnuchin and White House chief of staff Mark Meadows worked through the weekend on the GOP proposal and agreed to meet with Pelosi and Democratic Senate leader Chuck Schumer at the speaker’s office late Monday for talks.

The Republicans come to the negotiating table delayed, due to disagreements within the party. Senate Majority Leader Mitch McConnell, R-Ky., said he wanted to hit “pause” on new spending after Congress approved a $2.2 trillion relief package in March. But Pelosi, D-Calif., took the opposite approach, swiftly passing a $3 trillion effort with heavy Democratic support.

McConnell, flanked by top GOP chairs Monday at the Capitol, unveiled his proposal. It provides $105 billion to schools and colleges, with the K-12 funds tilted toward campuses that reopen with in-person learning. There’s more money for virus testing, $15 billion for child care centers and benefits for businesses, including a fresh round of loans under the Paycheck Protection Program, tax breaks and a sweeping liability shield from COVID-19-related lawsuits.

The Republican proposal would also provide another round of $1,200 direct payments based on the same formula from the earlier aid bill. People making $75,000 or less would receive the full amount, with the benefit phased out for those earning above $99,000, or double for married couples filing joint taxes.

It also provides $1.7 billion for a new FBI headquarters in Washington, a non-pandemic-related expense that’s a top priority of the president but not of lawmakers or McConnell.

“Senate Republicans have offered another bold framework to help our nation,” McConnell said. He called it a starting point in talks.

Some conservative Republicans disagreed with McConnell’s plan, arguing the spending was too much and priorities misplaced. Up to half the Republican senators could vote against the bill, some warned, and their opposition leaves McConnell heading into negotiations with Pelosi without the full force of the Senate majority behind him.

“The focus of this legislation is wrong,” Sen. Ted Cruz, R-Texas, one of the bill’s opponents, told reporters at the Capitol. “Our priority, our objective, should be restarting the economy.”

As bipartisan talks unfold, the White House is now suggesting a narrower relief package may be all that’s possible with Friday’s approaching deadlines.

Mnuchin and Meadows, in appearances Sunday, cited unemployment benefits, money to help schools reopen, tax credits to keep people from losing their jobs and lawsuit protections for schools and businesses as priorities for quick relief.

“We can move very quickly with the Democrats on these issues,” Mnuchin said.

Pelosi has resisted tackling a relief package in a piecemeal fashion, arguing that broader aid is needed for Americans. She disagreed with the Trump administration’s desire to reduce the $600 weekly unemployment aid to ensure no more than 70% of prepandemic wages.

“Children are hungry, families cannot pay the rent, unemployment is expiring and the Republicans want to pause again and go piecemeal,” Pelosi said.

“We have stood ready to negotiate for more than two months,” she said. She urged them to come to her office “and get the job done.”

The $600 weekly jobless benefits boost, approved as part of the March aid package, officially expires July 31, but because of the way states process unemployment payments, the cutoff was effectively Saturday.

Under the GOP proposal, the jobless boost would be reduced to $200 a week for two months through September and phased out to a new system that ensures no more than 70% of an employee’s previous pay. States could request an additional two months, if needed, to make the transition.

Friday is also the end of a federal eviction moratorium on millions of rental units that the White House said it wants to extend in some fashion.

Tuesday evening, Meadows said talks on the relief bill are “still in the second inning,” and that Democrats indicated they are unwilling to negotiate down their demand for extending the $600 a week unemployment benefit.