The bailout bill also expanded eligibility for unemployment benefits to include many self-employed and part-time workers. But only 10 states are approving applications from such workers, according to the Labor Department. Ohio has said it won’t start until May 15.

The problems may be worst in Florida, which implemented a series of changes over the past decade to make it harder to qualify for unemployment benefits, thus allowing the state to reduce taxes on businesses. The state’s online filing system, outsourced in 2011, has crashed repeatedly, forcing hundreds of workers to wait in long lines to file in person. Even among those who have completed the process and qualified for benefits, the state said Thursday, only 17 percent have received any money. And the maximum weekly benefit of $875, including the federal government’s $600, is among the lowest in the nation.

The federal government, meanwhile, is struggling to distribute stimulus payments of $1,200 to most American adults. The money has reached a little more than half of those who are eligible — but those still waiting tend to be the people who need it most.

People who did not file tax returns for 2018 or 2019 — including roughly 10 million American families whose incomes were so low that they were not required to file — will not get stimulus payments unless they submit an application to the I.R.S. The Trump administration has made little effort to contact such people, although some states are trying to fill the void: New York, for example, is teaming up with community groups to spread the word.

The administration has taken other steps to increase distribution — for example, by deciding to send checks automatically to people who already get other kinds of government benefits, like Social Security. But it announced earlier this week that such recipients needed to complete an online form to get extra payments of $500 for any dependent children.

It also announced that most people had less than two days to file the form — a deadline that passed on Wednesday. Congressional Democrats are pressing Treasury to reopen the application process. Otherwise, the decision, which affects households with roughly one million children in total, means many will not receive the money Congress voted to give them.

The government’s bailout program for small business suffers similar problems. Congress provided $349 billion in late March, which experts warned was grossly insufficient. Indeed, just 1.6 million companies — or about 26 percent of eligible small businesses — received aid before the money was exhausted. And the winners tended to be larger firms.