The Treasury Department will ask Congress for $200 billion more to aid small businesses, according to a person familiar with the matter, and Senate Majority Leader Mitch McConnell said the Senate could act as soon as this week to provide additional money.

Businesses have rushed to tap the $350 billion Paycheck Protection Program that was part of the massive $2.2 trillion stimulus passed by Congress in response to the economic crisis spawned by the coronavirus pandemic.

Stay-at-home orders across the country have particularly squeezed small businesses, which account for almost half of U.S. private employment.

Read more: What small businesses applying to the SBA’s Paycheck Protection Program need to know

McConnell said the Senate could approve more funding for the program during Thursday’s pro-forma session by voice vote or unanimous consent, which would allow almost all members to stay home.

“Congress needs to act with speed and total focus to provide more money for this uncontroversial bipartisan program,” McConnell said Tuesday, without giving a figure for the funding.

He said he was working with Treasury Secretary Steven Mnuchin and Senate Minority Leader Chuck Schumer on a proposal, though Schumer spokesman Justin Goodman said McConnell had yet to speak to Schumer. Moving quickly would require support from all Senate Democrats.

Schumer, just minutes earlier, had unveiled his own massive “Heroes Fund” to give hazard pay of up to $25,000 each for workers including grocery store employees, transit workers and pharmacists who are risking their lives to stay on the job amid the coronavirus outbreak. That is also likely to have a price tag in the hundreds of billions of dollars.

House Republican leader Kevin McCarthy said that he had spoken to Mnuchin and would support a request for additional money for the small business programs, saying that the House should act “swiftly” on the request.

House Speaker Nancy Pelosi hasn’t weighed in, but she previously called for an extension of the PPP program as part of a next round of stimulus that also would include an unemployment insurance extension, more direct payments and relief for states and localities. She has estimated the bill would cost at least $1 trillion.

Republicans have thus far been reluctant to enact a wide-ranging phase four stimulus bill. Now that they and their core business supporters such as the U.S. Chamber of Commerce are demanding an infusion for PPP, Democrats could have leverage to obtain more unemployment insurance and direct payment for workers. Pelosi would have to weigh such an opportunity against the political costs of delaying aid to small businesses.

GOP Senator Marco Rubio, chairman of the Small Business Committee, said he asked Mnuchin to make a formal request for at least $200 billion more for the program as soon as possible.

“There is a critical need to supplement the fund to ensure America’s more than 30 million small businesses will be able to access this critical lifeline,” he said in a statement.

White House Economic Adviser Larry Kudlow said on Fox News on Tuesday morning that as of Monday evening, about 178,000 loans for $50 billion had been processed. That amount hasn’t been given to businesses yet but rather is the value of loans SBA has registered and guaranteed for lenders to complete the process and disburse funds, according to a senior administration official.

More must-read personal finance coverage from Fortune:

—What to do if you can’t pay your bills this month
—Everything you need to know about the coronavirus stimulus checks
—5 things to know about unemployment benefits in the COVID-19 stimulus package
—Everything you need to know about furloughs—and what they mean for workers
—Everything you need to know about the new 401(k) no-penalty withdrawals
—Listen to Leadership Next, a Fortune podcast examining the evolving role of CEO
—VIDEO: 401(k) withdrawal penalties waived for anyone hurt by COVID-19

Subscribe to Fortune’s Bull Sheet for no-nonsense finance news and analysis daily.