The Kentucky Republican, who has supported about $500 billion in new aid spending, said he wants to pass what he called a "targeted relief bill" this year. McConnell said he spoke to White House officials about what President Donald Trump would sign into law. He plans to offer potential solutions to GOP senators and get their feedback.
"We just don't have time to waste time," he told reporters in response to the roughly $908 billion plan put together by bipartisan members of the GOP-controlled Senate and Democratic-held House.
McConnell said a must-pass spending bill and pandemic relief provisions will "all likely come in one package." Congress needs to approve funding legislation by Dec. 11 to avoid a government shutdown.
The framework of the bipartisan relief bill released Tuesday includes $288 billion in small business aid such as Paycheck Protection Program loans, $160 billion in state and local government relief, and $180 billion to fund a $300 per week supplemental unemployment benefit through March. It would put $16 billion into vaccine distribution, testing and contact tracing, funnel $82 billion into education, and put $45 billion into transportation. It would allocate funds for rental assistance, child care and broadband.
The proposal would not include another direct payment to most Americans. It also would offer temporary federal protection from coronavirus-related lawsuits — a provision Democrats have opposed — while states determine their own laws.
Democratic Sen. Mark Warner of Virginia, a member of the congressional group that has discussed a new relief plan, earlier called it an "interim package" to provide support until President-elect Joe Biden takes office in January.
"If there's one thing I'm hearing uniformly it's: 'Congress, do not leave town for the holidays leaving the country and the economy adrift with all these initial CARES [Act] programs running out,'" Warner told CNBC's "Squawk Box" on Tuesday.
It is unclear whether lawmakers can craft a plan that can get through both chambers of Congress before the end of the year, when many programs expire. Democrats have opposed liability protections and pushed for a $600 per week supplemental jobless benefit, while the GOP is against new state and local aid.
Sen. Joe Manchin, D-W.Va., who worked on the proposal, said the group had no assurances from House Speaker Nancy Pelosi, D-Calif., or Senate Majority Leader Mitch McConnell, R-Ky., that they would vote on the plan.
Still, the proposal's release underscored the rumbling among rank-and-file lawmakers to pass more aid even as party leaders fail to break a monthslong impasse.
"It is absolutely essential that we pass emergency relief," said Sen. Susan Collins, a Maine Republican who worked on the plan, at a news conference announcing the proposal.
The pandemic has rampaged through the country, straining hospitals and forcing state and local officials to implement new business restrictions to slow infections. At the same time, lifelines put in place by Congress earlier this year will expire at the end of 2020 hitting Americans already struggling to cover costs.
The programs lapsing at the end of December include an unemployment insurance extension, a federal student loan payment moratorium and eviction protections.
Pelosi and McConnell have not yielded ground from their respective $2.2 trillion and $500 billion aid bills. Leaders of the Democratic-held House and GOP-controlled Senate have not held formal talks on stimulus since the 2020 election on Nov. 3.
Talks between the Trump administration and Democrats collapsed before the election. On Tuesday, Pelosi and Treasury Secretary Steven Mnuchin spoke for the first time since late October.
After the call, Pelosi said Mnuchin told her he would review a proposal she and Senate Minority Leader Chuck Schumer, D-N.Y., sent to Republicans on Monday. She did not specify what the plan includes. Mnuchin also said he would look over the bipartisan plan put out Tuesday, according to Pelosi.
"Additional COVID relief is long overdue and must be passed in this lame duck session," she said in a statement.
Mnuchin said during congressional testimony Tuesday that he spoke with McConnell, Trump, House Minority Leader Kevin McCarthy, R-Calif., and White House chief of staff Mark Meadows. They agreed that Congress should craft a targeted fiscal response, he added. The Treasury secretary said he wants to focus on "what we can pass quickly on a bipartisan basis" to get relief to "the most difficult parts of the economy."
During the stalemate, members of both parties have urged compromise to ease some of the pressure on the economy and health-care system. On top of the economic programs, the federal government will likely need to approve funds to streamline distribution of Covid-19 vaccines in the coming months.
Senators who have joined in the discussions about the aid proposal include Warner, Collins, Manchin, Sen. Lisa Murkowski, R-Alaska, Sen. Mitt Romney, R-Utah, Sen. Maggie Hassan, D-N.H., and Sen. Bill Cassidy, R-La. House members including Democratic Rep. Josh Gottheimer of New Jersey and Republican Rep. Tom Reed of New York, leaders of the Problem Solvers Caucus, were also involved.
Federal Reserve Chair Jerome Powell has also repeatedly called on Congress to send more fiscal relief to boost the economy. Asked about the aid proposal during congressional testimony Tuesday, he said it seemed the plan targets "a lot of the areas that could definitely benefit from help" and will "be experiencing a challenging winter."
If the unemployment programs expire at the end of the year, about 12 million Americans could lose benefits. The two policies allow people to receive insurance for longer than they normally would and make freelance workers, contractors and others who normally would not qualify for benefits eligible to receive them.
Warner led a letter from about 30 Democratic senators to the chamber's leadership on Tuesday calling to extend both policies. They wrote that the loss of benefits around Christmas would be "particularly cruel," especially as the outbreak is expected to worsen in the winter months.
— CNBC's Ylan Mui and Jeff Cox contributed to this report