The government has only started the rapid, at times rocky implementation of the largest emergency spending package in U.S. history. Designed to bolster resources for an overburdened health-care system and blunt economic destruction as COVID-19 spreads, the law includes strengthened unemployment benefits, $350 billion in small business loans and $500 billion in loans and grants for companies, states and municipalities, among other measures.

"The appetite is there," he said in a CNBC "Squawk Box" interview. "I think everyone I've talked to recognizes we're going to have to go back and do more, and probably more than once."

The Florida Republican, chairman of the Senate Small Business and Entrepreneurship Committee, said Congress will likely have to expand pieces of the $2 trillion stimulus package passed last month. Rubio expects an additional recovery bill after lawmakers assess the wreckage the outbreak leaves in its wake.

Senators acknowledge they will have to pass another emergency bill to limit the damage from the coronavirus pandemic, Sen. Marco Rubio said Monday.

The pandemic's effects have only started to emerge. The U.S. has at least 337,600 cases of COVID-19, and at least 9,648 deaths have been linked to the disease, according to data compiled by Johns Hopkins University. Already, roughly 10 million people have filed new unemployment claims as businesses shut down to prevent more infections.

As coronavirus tears across the country, Rubio expects more action from Congress — including to reload the small business program he helped to craft.

"I believe Congress is going to have to go back in some way, shape or form and address additional things that have emerged since [the first bill passed]," he said. "That includes, by the way, replenishing the funds on the small business loan program. Because I believe that those funds, given the demand, will not reach June 30."

Lenders started to accept applications for small business loans on Friday, only a week after the emergency relief bill became law. Both loan seekers trying to cover rent and keep employees on the payroll, and the banks doling out the money, expressed frustration about the program's rollout.

Rubio acknowledged issues but said, "It will get better. It has to get better."

In recent days, congressional leaders have outlined what they want to see in an additional relief bill. House Speaker Nancy Pelosi is pushing for another bipartisan bill that builds on the $2 trillion package, with more direct payments to individuals, additional small business funding, an extension of the enhanced unemployment insurance and more state health-care grants.

She hopes to move legislation forward after the House returns on April 20, she told members in a letter Saturday.

Senate Majority Leader Mitch McConnell said Friday that the next bill should address the shortcomings of the last legislation, starting with the health-care response. But the Kentucky Republican told The Associated Press he is "not in favor of rushing" to the next phase before he sees how effective the previous bill is.

Rubio said Monday that the "bigger challenge" in passing a bill is "logistical." Members of Congress are currently working from their states and districts, fearing a return to Washington as the number of lawmakers presumed to have COVID-19 grows.

Congress can pass bills unanimously with a few people in the Capitol. But opposition from only one member can blow up those efforts — as seen when Rep. Thomas Massie's objection to a unanimous vote forced House members to rush to Washington to pass the $2 trillion relief package last month.

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