Washington (CNN) Senate Republicans are racing to reach a GOP deal on a massive $1 trillion economic stimulus as the coronavirus crisis intensifies, despite facing criticism from Democrats who warn that efforts to swiftly pass a stimulus could be derailed if they are not included in negotiations now.

Senate Majority Leader Mitch McConnell on Wednesday said Republicans are "getting close" to a deal and has outlined a plan that would involve Republicans coming to an agreement before going to Democrats in an attempt to forge a bipartisan consensus.

The legislative package is on track to become the most significant congressional action in response to the pandemic that has temporarily closed schools, businesses and ground travel to a halt. The proposal comes on the heels of two major pieces of legislation that lawmakers have pushed to address the growing crisis -- and all told amounts to the most far-reaching economic rescue packages since the financial crisis in 2008.

In a sign of tension between Republicans and Democrats, however, Senate Minority Leader Chuck Schumer criticized the way that Senate Republicans are negotiating on the economic package on Wednesday, calling for them to do more to include Democrats.

"Phase three legislation should be the product of a five corners negotiation," the New York Democrat said. "House and Senate leaders, majority and minority, plus the White House."

"The process that Leader McConnell has outlined," Schumer said, "is too cumbersome, too partisan and will take far too long given the urgency and need for cooperation."

House Speaker Nancy Pelosi made a similar point during a conference call on Wednesday with House Democratic leadership and committee chairs of jurisdiction focused on next steps for coronavirus response.

According to an aide on the call, Pelosi expressed her view during the call that the quickest way to get a third legislative package finished by early next week would be to have a four corners negotiation.

But McConnell on Wednesday threw cold water on Pelosi's call to let the top leaders of Congress on both sides sit down and cut a deal on the massive stimulus plan.

Asked by CNN about Pelosi's suggestion, McConnell said the process should look like this: Senate Republicans will get a deal among themselves and then they will negotiate with Schumer, whom he said "will keep the Speaker in the loop."

"I anticipate what I've said repeatedly, which is we're in a process of deciding exactly where we are and where the administration is-- and then we obviously intend to sit down with Sen. Schumer. And I'm sure he will keep the speaker in the loop and we'll move to getting a bipartisan agreement," McConnell said.

The Senate approved a House-passed coronavirus relief package on Wednesday, paving the way for the chamber to devote its full attention to the economic stimulus package that lawmakers are referring to as "phase three" in their response to the pandemic.

But Democrats and Republicans are not yet on the same page, signaling hard-fought negotiations ahead.

Republicans meet over proposal

At a lunch meeting, GOP senators presented their proposals that would comprise the $1 trillion stimulus, and Republicans emerged saying an agreement would be reached internally Wednesday or Thursday.

"We are getting close," McConnell told reporters. "We are working along and hoping to be together shortly."

At the meeting, the Kentucky Republican told each of the groups of GOP senators tasked with putting together proposals for the stimulus to submit their plans by Thursday morning, according to GOP Sen. Marco Rubio of Florida.

Rubio said his component -- for $300 billion in relief for small businesses - will be done by tonight.

After the lunch, Sen. Shelley Moore Capito of West Virginia said that each of the groups appear to be in agreement about individual proposals.

Once an internal agreement is set, the GOP will begin negotiating with Democrats to see if a bipartisan deal can be reached. But Democrats have their own plans and it is not yet clear how they will be reconciled with Republican proposals.

The rush to put together a GOP deal comes as lawmakers are scrambling to contain the economic and public health fallout from the rapid spread of the coronavirus across the United States.

The urgency has led to Republicans expressing support for a staggeringly high funding level, a package that one treasury memo suggests could include a combined $500 billion in checks to Americans to address the economic impact of the coronavirus.

Sen. Ron Johnson, a Wisconsin Republican who has railed against debts and deficits since he became a senator, said he was "encouraged" about what he heard but that there will ultimately be a lot about the plan that he'll "hate."

Sen. Josh Hawley, a Missouri Republican, said he's concerned about bailouts for the airlines but said that he wouldn't characterize what he's hearing as a bailout.

GOP Sen. Todd Young of Indiana said that "We will start to see some details today" from the task forces. He said there is a great sense of "urgency" among all Republicans "to get something to the floor to vote on, to reassure people they will have paychecks."

CNN has obtained a two-page memo from the US Treasury detailing its recommendations for the phase three coronavirus stimulus package. Republican senators are working off of the memo as they draft their own proposal.

The Treasury memo breaks the nearly $1 trillion package down into four main categories, including a category for direct payments to taxpayers split into two rounds of $250 billion each. The memo states that the first round of payments would be issued starting on April 6.

The plan's massive price tag underscores the growing fears in the White House and on Capitol Hill that the coronavirus outbreak could send the economy into a damaging recession -- and that aggressive intervention by Washington is needed immediately to reverse course. Already, lawmakers have pushed two major pieces of legislation to address the growing crisis.

Senate may work through the weekend

McConnell has vowed to keep the Senate in session until a stimulus package is passed.

Two Senate Republican leaders said Wednesday that the Senate won't be able to complete action on the $1 trillion-plus package before next week and will work through the weekend to try to hammer out a deal with Democrats.

Asked if the Senate could pass a bill as early as Thursday -- an ambitious time frame some GOP senators said they hoped to meet -- Republican Sen. John Cornyn of Texas was dubious it could be done that quickly.

"I think it's going to take a little longer than that. I would say early next week. We will get the first bill done today. The President will sign it. And then we'll turn our full attention to the next install," Cornyn said.

Sen. John Thune of South Dakota, the Republican whip, agreed.

"We're trying to accelerate everything, pull it together quickly. But by the time you get into negotiations with the Democrats, it pushes it through the weekend," Thune said. "We'll see what happens. As you know around here, when there's a sense of urgency things can happen more quickly."

McConnell declined to say if he agreed it would take into next week.

But after the Senate passed phase two of the coronavirus relief efforts, McConnell went to the floor and urged senators not to leave town as negotiations ramp up on phase three.

"I would recommend senators stay around, close. Just how long it will take to get through these steps is unclear but as everyone knows, we are moving rapidly because the situation demands it," McConnell said.

This story has been updated with additional developments Wednesday.