If the shutdown uses up the rest of his savings, he said he planned to “pull out the credit card.”

Alecia Lane, a management analyst at the Food and Drug Administration who has been furloughed since Dec. 27, said she budgeted her expenses carefully and did not know how loan payments would fit into them once her paychecks returned.

“That’s another bill added that people might not be able to afford,” she said.

Ms. Lane preferred a crowdsourced solution: She set up a GoFundMe account. The page, which went up Friday, asks for $5,000 — the amount she has missed over two pay periods. As of late Thursday, she had raised over $3,000.

Demand for loan programs can only increase as the shutdown drags on. Navy Federal Credit Union said about 100,000 of its 8.1 million members were affected by the shutdown. More than 19,000 had enrolled in its loan program, and the number was rising.

Tynika Wilson, senior vice president for debit cards and funds services, said the credit union had decided to extend its program for a second pay period, but was “re-evaluating and reassessing as things are unfolding.”

If the shutdown persists, some of these institutions could end up needing loans themselves.

The U.S. Employees Credit Union, based in Chicago, is offering interest-free loans to the federal workers who make up the vast majority of its 8,000 members.

The credit union has $85 million in assets under management, but as of two weeks ago, the total dollar amount of direct deposits it received had dropped nearly 30 percent.

“We have enough capital to survive like this for another four or five pay periods without having to do some serious borrowing,” said Eric W. Stiegel, the credit union’s president and chief executive. “We are hoping that doesn’t happen.”