The administration warned lenders on Wednesday that it would soon be unable to accept any new loan applications or applications to be lenders once the funds ran out.

The stimulus law included $349 billion for the Paycheck Protection Program, which underwrites bank loans for small businesses that will never need to be repaid if owners use most of the money to keep paying employees for two and a half months. Economists and business lobbyists warned when the bill was being debated that the money was nowhere close to the $1 trillion or more that companies would need.

“We always knew we would have to come back and replenish it — we thought we were going to have an outreach problem, letting people know that this program existed,” said Mr. Rubio, the chairman of the Senate Committee on Small Business and Entrepreneurship.

“It’s an ironic situation, because everyone’s in favor of it,” he said of the program. “I just want to see action.”

Democrats say that while they support supplying the program with additional aid, there remain challenges in ensuring that all businesses are not only receiving the loans, but the actual funds themselves.

“It’s a critically important thing to accomplish — you want to be able to allow the small businesses to jump start on the other side of this,” said Representative Antonio Delgado of New York, whose upstate district is one of the most rural counties represented by a Democrat. He added, “the challenge has been having people access these funds.”

Early evidence suggests that the efforts have disproportionately helped manufacturers and construction firms at the expense of the hospitality businesses — including restaurants, bars and hotels — that have suffered the highest rates of job loss in a month in which nearly 17 million Americans have filed for unemployment. The loans are allocated on a first-come, first-served basis, an approach that has favored businesses that have existing relationships with lenders and the resources to navigate the government application process.