It is a common reaction to the unusual role that the Small Business Administration plays in disaster recovery. The agency, best known for its business loan programs, is the federal government’s main avenue for providing quick cash to help victims repair or replace damaged housing and property after a disaster.

FEMA provides some short-term aid for urgent needs — such as medical help and temporary housing — but it steers applicants toward the S.B.A.’s disaster loans for long-term recovery help.

Renters and homeowners are eligible for S.B.A. loans of up to $40,000 to cover property losses, and homeowners can borrow up to $200,000 for repairs to real estate. The rates on those loans range from 1.75 percent to 3.5 percent — far lower than other options like credit cards or bank loans — and the terms on them can stretch as long as 30 years.

But the idea of receiving cash — and then a bill for it later — is often unappealing to those facing a precarious financial future.

“I’m not taking the loan until we know if we can pay it back,” Mrs. Moyer, 43, said in an interview. She is retired, and her husband was laid off shortly before the storm. “If I don’t take the money, then what happens to disaster relief for me?”

That reckoning is familiar to many who have experienced past disasters.

Five years after Hurricane Sandy ravaged coastal areas in New York and New Jersey, many residents and business owners in affected neighborhoods are still trying to collect all of the assistance they had been promised.

“It’s become a monstrosity,” Michele Insinga, executive director of Adopt a House, a nonprofit recovery group in Lindenhurst, N.Y., said of the bureaucracy that developed around Sandy relief. “There are so many horror stories from people who are still putting their lives back together.”

Beth Henry, 44, had her two-story home in Massapequa, N.Y., destroyed when Sandy flooded it with three feet of water. She qualified for an S.B.A. disaster loan, but found that it would cost her more than $900 a month to repay it.

“I’m not sure who can pay that kind of loan, on top of their mortgage,” Ms. Henry said.

She instead borrowed from her family and drained her savings while wrangling with her flood insurance carrier — the National Flood Insurance Program, a federal program troubled by insufficient funding. In the end, she collected just $51,000 from the program, far less than it had cost her to rebuild.

Because Ms. Henry qualified for an S.B.A. loan, she was ineligible for any grants from FEMA to offset the cost of repairing her home. She eventually received help from another federally funded Sandy-relief program, the NY Rising Community Reconstruction Program, but the $36,371 she collected from that grant came nearly two years after the storm.

“The money was not free-flowing,” Ms. Henry said. “It was a real battle, and a long one.”

For Harvey’s survivors, that battle is just beginning. Even for those who choose not to take an S.B.A. loan, applying for one is often a necessary first step. The agency said it had received 253 applications from those affected by the storm, and the department’s administrator, Linda McMahon — who traveled with President Trump to Texas on Tuesday — said that at least one home repair loan had already been approved.

But for Mrs. Moyer, the red-tape-wrapped bureaucracy of federal aid feels like a second disaster in the making.

On Wednesday, FEMA asked her to return to her destroyed home, hours away from where she is staying, to meet with an inspector. At the same time the S.B.A. requested that she print and fax in her loan application — which would require her to find a printer and a fax machine in the middle of a disaster. (The agency said people will be able to apply in person through FEMA recovery centers, but none had opened yet in the places affected by Harvey.)

“I’m just really losing it,” Mrs. Moyer said. “I loved this town and it’s just gone — it’s like a war zone. It’s just too much.”