Pressure is building on Congress to pass another round of coronavirus relief legislation, but Republicans and Democrats have different ideas about what’s needed and how fast.

Democrats want to move swiftly while GOP aides warn it’s unlikely a fourth bill will pass before May.

In a bid to give Congress more time to deliberate before passing another massive relief bill, Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellMcConnell focuses on confirming judicial nominees with COVID-19 talks stalled McConnell accuses Democrats of sowing division by 'downplaying progress' on election security Warren, Schumer introduce plan for next president to cancel ,000 in student debt MORE (R-Ky.) says he will ask for unanimous consent Thursday to provide as much as $250 billion in additional money to help small businesses keep workers on the payroll. The program, for which Congress appropriated nearly $350 billion in the enacted $2.2 trillion CARES Act, is highly popular and faces an imminent shortfall of funding.

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In a telling tactical decision, however, McConnell did not reach out to Senate Minority Leader Charles Schumer Chuck SchumerMcConnell accuses Democrats of sowing division by 'downplaying progress' on election security Warren, Schumer introduce plan for next president to cancel ,000 in student debt Schumer lashes out at Trump over 'blue states' remark: 'What a disgrace' MORE (D-N.Y.) — nor did Small Business Committee Chairman Marco Rubio Marco Antonio RubioFlorida senators pushing to keep Daylight Savings Time during pandemic Hillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll Intelligence chief says Congress will get some in-person election security briefings MORE (R-Fla.) reach out to his counterpart, Sen. Ben Cardin Benjamin (Ben) Louis CardinPPP application window closes after coronavirus talks deadlock Congress eyes tighter restrictions on next round of small business help Senate passes extension of application deadline for PPP small-business loans MORE (D-Md.) — prior to announcing Tuesday that Republicans would seek the influx of small business funding by unanimous consent. Rubio and Cardin worked closely to help craft the unprecedented small-business program.

Republican leaders expect that Schumer will attempt to attach any of a number of Democratic priorities to the request, such as up to $25,000 in hazard pay for essential workers, including doctors and nurses as well as grocery store clerks, GOP aides say.

McConnell on Tuesday warned that any legislation Congress passes next should be focused on fixing oversights of the CARES Act, which President Trump Donald John TrumpHR McMaster says president's policy to withdraw troops from Afghanistan is 'unwise' Cast of 'Parks and Rec' reunite for virtual town hall to address Wisconsin voters Biden says Trump should step down over coronavirus response MORE signed into law March 27, instead of bold liberal proposals favored by Schumer and Speaker Nancy Pelosi Nancy PelosiMcConnell focuses on confirming judicial nominees with COVID-19 talks stalled Overnight Defense: Top admiral says 'no condition' where US should conduct nuclear test 'at this time' | Intelligence chief says Congress will get some in-person election security briefings Pelosi must go — the House is in dire need of new leadership MORE (D-Calif.).

“As the administration works to implement this historic legislation and push money out the door, Senate Republicans believe any potential further action will need to be tailored to the actual needs of our nation, not plucked off preexisting partisan wish lists,” McConnell said Tuesday.

Treasury Secretary Steven Mnuchin Steven Terner MnuchinMcConnell focuses on confirming judicial nominees with COVID-19 talks stalled Hillicon Valley: FBI chief says Russia is trying to interfere in election to undermine Biden | Treasury Dept. sanctions Iranian government-backed hackers On the Money: Pelosi draws line at .2T | Jobless claims dip | Swing-state jobless numbers an issue for Trump MORE on Tuesday asked Congress to appropriate another $250 billion to the fast-diminishing small-business program that will forgive loans as long as employers keep workers on their payrolls. In the past two weeks, a record 10 million Americans have filed unemployment claims.

The administration says banks have already processed $70 billion in federally backed loans for more than 200,000 small businesses. Many small businesses are still waiting on federally guaranteed aid.

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Asked Tuesday if he would insist on adding hazard pay for essential workers to small-business funding, Schumer said the “Heroes Fund” is one “of our very highest priorities in COVID-4,” referring to the fourth relief bill.

If Schumer allows the extra small-business funding to pass by unanimous consent, he’ll give up a powerful bargaining chip. But if Democrats block the request, it could give them a public relations black eye. A spokesman for Schumer did not respond to a request for comment on the issue.

Schumer, Cardin and other Senate Democrats sent a letter to the Small Business Administration on Tuesday to ask Administrator Jovita Carranza and Mnuchin to reserve a portion of the small-business lending program for businesses owned by veterans, minorities and women.

Democrats are pushing for other priorities as well, such as additional funding to shore up state and local government budgets and an expansion of the Affordable Care Act’s enrollment window for the uninsured.

Republican leaders want to postpone a larger relief package beyond this month, so the administration has time to implement and Congress has time to assess the CARES Act.

There’s growing skepticism among Senate aides about whether Congress will even reconvene in Washington the week of April 20 as expected, when coronavirus infections are projected to be nearing their peak in the United States.

Senate Republicans say the small-business funding boost should move quickly and separately.

One senior Senate GOP staffer said it’s “premature” to start negotiating another coronavirus relief bill when the third bill “is not even two weeks old yet.” The aide noted that funding for state governments isn’t scheduled to go “out the door” until April 24 and that a myriad of other aid programs has yet to get up and running.

“We’re focused on seeing how implementation goes and taking stock of the epidemic. The peaks of infection are coming down because of social distancing and the effectiveness of the quarantines,” the aide said. “We’re taking stock of what’s actually needed. This isn’t a Clyburn moment to take advantage of a crisis.”

House Majority Whip James Clyburn (D-S.C.) told Democratic colleagues in a conference call last month that the expected rounds of economic stimulus legislation are “a tremendous opportunity to restructure things to fit our vision.”

Schumer and Pelosi have been urged by their respective caucuses to seek more money for state and local governments, vote-by-mail programs, student debt relief, Social Security benefits and cash-strapped employer-provided pension programs.

At the same time, McConnell and House Minority Leader Kevin McCarthy Kevin Owen McCarthyTrump's sharp words put CDC director on hot seat House GOP leader says he trusts Trump over CDC director on vaccine timing The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Trump contradicts CDC director on vaccine, masks MORE (R-Calif.) have to contend with conservative colleagues who are disgruntled by elements of the second and third coronavirus relief laws, such as mandated paid sick leave and beefed-up unemployment benefits that in some states may exceed 100 percent of a worker’s regular pay check.

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McConnell called on his colleagues to “gag and vote for” the second bill, drafted by House Democrats — projected to cost more than $100 billion — which included the paid sick leave provisions because the nation was in crisis. McConnell later said it was necessary for “the sake of building bipartisan momentum.” The Senate then took the steering wheel on the CARES Act.

Republican lawmakers viewed it as imperative to pass the largely Senate GOP-drafted bill as quickly as possible under threat of a precipitous collapse of stock prices.

Now, however, Senate Republicans say the scenario is different, as the rate of new coronavirus infections is starting to stabilize, and Trump proclaimed Sunday there’s “light at the end of the tunnel.”

Sen. Rob Portman Robert (Rob) Jones PortmanRomney undecided on authorizing subpoenas for GOP Obama-era probes Congress needs to prioritize government digital service delivery House passes B bill to boost Postal Service MORE (Ohio), one of the GOP authors of the CARES Act, says Congress should take its time on the next bill.

“The fact is we’ve got to be sure we aren’t wasting money,” he told “The Hugh Hewitt Show” on Monday. “We’ve got to make sure we’re spending money properly.”

The senior GOP aide said, “everybody knows there’s going to need to be a 4.0 [bill].”

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“We’re going to need to give more money to hospitals and health care professionals. We’re going to have to give more money to states and locals, we’re going to have to give more money to schools. But it’s not like the market is saying, ‘Oh my God, when is 4.0 coming?’ ” the aide said. “There’s not as much urgency to doing a 4.0 right now.”

A second Senate GOP aide said they “can’t imagine anything big getting through this month,” adding, “I doubt that we’ll be back on the 20th.”

McConnell told The Associated Press last week “there will be a next measure” but cautioned he didn’t want to rush into passing another bill before lawmakers had a chance to assess the impact of the CARES Act.