The federal government fumbled the reboot of the popular Paycheck Protection Program on Monday, with bankers saying just a fraction of loan applications managed to get through a balky system at the U.S. Small Business Administration.

"We heard from small banks, large banks and midsize banks that they all had a ton of trouble," said Joe Witt, president of the Minnesota Bankers Association. "It was an equal-opportunity problem, unfortunately."

Some banks spent hours trying to get a single application through the system. Others sent their lending teams home during the day and told them to come back in the middle of the night to improve their chances of connecting with the SBA.

"It was a very frustrating and challenging rollout," said Paul Merski, executive vice president of the Independent Community Bankers of America, a trade group that represents 5,000 small and midsize financial institutions.

As of Tuesday afternoon, nearly 476,000 loans totaling approximately $52.2 billion were processed and approved by the SBA.

"Unprecedented demand is slowing our system response times," SBA Administrator Jovita Carranza said in a tweet Monday. "Currently, there are double the number of users accessing the system compared to any previous day during the first round of Paycheck Protection Program funding."

Firms with 500 or fewer employees can obtain up to $10 million through the program, and the loans are forgiven if companies rehire all furloughed employees by June 30 and meet other requirements.

Executives at smaller community banks complained about SBA rule changes that seem to favor large institutions and their small-business customers. Most of the country's largest banks erected barriers to noncustomers during the first $349 billion round of funding, which led to allegations that the process was tilted in favor of well-connected companies who were able to scoot to the front of the line while smaller firms were left stranded when the money ran out.

Congress allocated another $310 billion to the program. The money is expected to be gone by the end of the week. The first round of funding lasted 13 days.

"Banks have been accepting applications and processing loans since the money ran out in mid-April, so there was a tremendous volume of loans just sitting there, ready to go," Merski said.

Florida Sen. Marco Rubio, chairman of the Senate's Small Business and Entrepreneurship Committee, estimated there were 800,000 applications on hold as of April 20.

With loans averaging $206,000 in the first round, that indicates that at least $165 billion in additional funding is already spoken for.

Noah Wilcox, majority owner of two community banks in Minnesota and chairman of the Independent Community Bankers of America, said big banks have an unfair advantage in the second round of funding because the SBA is accepting bulk submission of application files.

The agency announced it would accept batches with a minimum of 15,000 applications on Sunday, but reduced that figure to 5,000 applications when the system repeatedly crashed on Monday.

Even at 5,000 applications in a batch, Wilcox said, the rules are clearly aimed at helping big banks, since the vast majority of smaller banks had hundreds of applications on file, not thousands.

"That is a backdoor key for the biggest banks in the country," Wilcox said. "There should be equal and equitable access to the system."

Executives at smaller institutions were also unhappy that the SBA was allowing banks to use robotic systems to submit applications files, an expensive process that is out of range for most community banks.

The SBA stopped accepting robotic applications Tuesday.

"I thought that was crazy," said John Stellner, president of Hometown Community Bank in Cyrus, Minn. "Let the little banks have a fair crack at it."

Andrea Roebker, communications director for the six-state SBA region that includes Minnesota, said the agency's decision to eliminate robotic applications will make the system "more reliable, accessible, and equitable for all small businesses."

To address complaints, Congress reserved $60 billion of the second round of financing for financial institutions with less than $50 billion in assets.

It also banned any single bank from loaning out more than $60 billion in PPP loans to prevent larger institutions from dominating the business.

That means some banks will be hitting the ceiling soon.

At Bank of America, the nation's second-largest financial institution, lenders accepted 390,000 applications totaling $50 billion in loans in the first round, according to spokeswoman Carla Molina.

She said the bank will process those requests before moving ahead with any new applications.