In a shift, Senate Majority Leader Mitch McConnell was preparing Wednesday to roll out a “handful” of COVID-19 aid bills instead of a single package as Republicans revolt and split from the White House over priorities, according to a top lawmaker involved in the negotiations.

"I think what the leader has decided he wants to do is to have a handful of bills now instead of just one bill, so maybe that comes together,” Sen. Roy Blunt, R-Mo., told reporters at the Capitol. He said the goal is to unveil those bills Thursday.

One holdup remains the tension between Republicans and the White House over President Trump's push for a payroll tax cut, which is not supported by many lawmakers. McConnell and some of his GOP colleagues prefer a second round of $1,200 payments.

The rest of the legislation is taking shape even as key Senate Republicans are rejecting the rescue's $1 trillion price tag, which is almost certain to grow. But McConnell is trying to push forward with what he calls a “starting point” in negotiations with Democrats.

“Very productive meeting,” Treasury Secretary Steven Mnuchin said while exiting a late session at the Capitol.

Exasperated Democrats warned the GOP infighting with Trump is delaying needed relief to Americans during the crisis, with the U.S. pandemic death toll climbing past 142,000.

Sen. Roy Blunt, R-Mo., left, and Senate Majority Leader Mitch McConnell of Ky., leave a news conference after a Republican luncheon, Tuesday, July 21, 2020, on Capitol Hill in Washington. (AP Photo/Jacquelyn Martin)

With millions out of work and a potential wave of evictions ahead, the severity of the prolonged virus outbreak is testing Washington's ability to respond. Schools are delaying fall openings, states are clamping down with new stay-at-home orders and the fallout is rippling through an economy teetering with high unemployment and business uncertainty. A new AP-NORC poll shows very few Americans want full school sessions without restrictions in the fall.

“We’re hopeful we’ll be able to get there,” McConnell told reporters earlier Wednesday.

Pressure is mounting as the virus outbreak deepens, and a $600 weekly unemployment boost and a federal eviction moratorium come to an end starting Friday. But the size and scope of the federal spending, and the jumble of competing priorities from Trump and GOP senators, left the outcome uncertain

Democrats, who already approved House Speaker Nancy Pelosi’s more sweeping $3 trillion package two months ago, said time is running out for Trump and his GOP allies to act.

“We’re still on the 20-yard line?” Senate Democratic Leader Chuck Schumer said, referring to White House comments. “Where have the Republicans been?”

"I just don’t see the need for it."

— Sen. Ron Johnson, R-Wis.

As the Republicans battle over their priorities, Democrats warn they are wasting precious time.

“We are just days away from a housing crisis that could be prevented,” said Sen. Elizabeth Warren, D-Mass.

McConnell’s blueprint is expected to include a new round of direct payments to earners below a certain income level, similar to the $1,200 checks sent in the spring. It also will likely have some version of Trump’s demand for a payroll tax holiday for workers, which many Republicans oppose.

Republicans said they want to replace the $600 weekly federal jobless benefit with a lower amount. Sen. Rob Portman, R-Ohio, said it would likely be swapped for one more closely pegged to state benefits rates. That means workers in states with larger benefits would get a more generous add-on.

“We cannot allow there to be a cliff in unemployment insurance given we’re still at about 11 percent unemployment,” Portman said.

Republicans want to include at least $105 billion for education, with $70 billion to help K-12 schools reopen, $30 billion for colleges and $5 billion for governors to allocate. The Trump administration wanted school money linked to reopenings, but in McConnell’s package the money for K-12 would likely be split between those that have in-person learning and those that don’t.

Sen. Marco Rubio, R-Fla., said there will be another boost for small business lending in the Payroll Protection Program. “It’s going to be big,” he said.

The centerpiece of the GOP package will be McConnell’s five-year liability shield to protect businesses, schools and others from COVID-related lawsuits. It’s also likely to include tax breaks to help shops and workplaces retool safely for the reopenings.

Mnuchin and Meadows made it clear during a private meeting Tuesday with Pelosi and Schumer that the White House was resisting Democratic proposals for new spending on virus testinghousing aid or money for cash-strapped states, according to a person granted anonymity to discuss the private talks.

Republicans said some $150 billion allotted previously to state governments is sufficient to avert sweeping layoffs, and they said more housing protections are not needed.

However, Democrats are calling for $430 billion to reopen schools, bigger unemployment benefits and direct aid checks, and a sweeping $1 trillion for state and local governments. They also want a fresh round of mortgage and rental assistance and new federal health and safety requirements for workers.

Congress approved a massive $2.2 trillion aid package in March, the biggest of its kind in U.S. history. Pelosi pressed on, passing her $3 trillion House bill in May. McConnell at the time said he wanted to “pause” new spending.

Fox News' Sally Persons and The Associated Press contributed to this report.