The current unemployment system in Florida dates back to 2011, when the state legislature and Mr. Scott, a Republican and the governor at the time, enacted a series of major changes. It was not long after the Great Recession, and the federal government had increased unemployment taxes on businesses. In response, the Republican-controlled legislature set out to reduce that benefit to be able to bring taxes back down.

Floridians, who once could file by phone, now had to file online, and faced a set of new electronic filing requirements that made the process of establishing eligibility one of the most onerous in the nation, Ms. Evermore said. The online system was hard to use, offered very little customer service and limited access for Spanish speakers. A cumbersome skills test had appeared. People had to prove, on a complicated online form, that they had applied to at least five jobs a week. Benefits went to as few as 12 weeks from 26.

The result was disastrous for unemployed Floridians. By 2015, just 39 percent of workers who applied for benefits ever received a first payment, compared with 68 percent nationally. That number has not changed much, Ms. Evermore said.

When the virus hit, Florida was at the bottom of the pack. Just 11 percent of unemployed Floridians were receiving unemployment insurance in 2019, compared with about 52 percent of unemployed people in Massachusetts and 57 percent in New Jersey, according to data from the Department of Labor. Florida was the second-worst in the country last year by a hair, just after North Carolina.

Mr. DeSantis said last week that the state was slow to process claims before the virus.

“If you applied in January, I mean, it was a cumbersome process — it would take several weeks,” he said. “But when the unemployment rate is 3 percent, it’s a little bit different than what we have now.”

This week, Mr. DeSantis sounded more exasperated: “Look, this system, the fact that the state paid $77 million for this thing — it’s a jalopy.”