“I think they have done a terrific job,” said Paul M. Rosen, who worked in the Obama administration as the former chief of staff at the Department of Homeland Security. “You just have to tune out the political noise and let them do their jobs.”

Strides Since Katrina

In 2005, FEMA became the face of the bungled federal response to Hurricane Katrina, and the agency’s poor handling of the disaster in New Orleans led to the resignation of Michael D. Brown, the director at the time. FEMA has since improved its image, and former federal officials praised its response in recent weeks to a staggering string of hurricanes, wildfires and other disasters. Over all, about 8,200 people in FEMA’s nearly 10,000-person work force are deployed in the field, responding to more than 20 natural disasters around the country.

“The whole response-and-recovery industry is maxed out,” said Michael Coen, the former chief of staff at FEMA in the Obama administration.

The Trump administration has been publicly criticized for its response to Hurricane Maria in Puerto Rico. While the problems there with power, gas and water are far worse than those in the continental United States, FEMA’s response to Harvey and Irma has also quietly frustrated flood victims on the mainland, from low-income neighborhoods to trailer parks to wooded suburban enclaves. Some have turned to their elected officials to complain and ask for help navigating the multiagency disaster bureaucracy, including FEMA’s federal insurance arm, which manages the National Flood Insurance Program.

In Kingwood, Tom and Lisa Slagle asked Senator Ted Cruz’s office for help after a $25,000 flood-insurance payment they were counting on was delayed for more than a month. “This has been more a disaster, trying to deal with insurance, than it was when our house flooded,” said Ms. Slagle, 49, a retired Houston firefighter.

In South Florida, officials in Collier County, which includes Naples, are waiting for FEMA R.V.’s known as travel trailers, which flooded residents can use as temporary housing. Only 15 of the trailers have been approved by FEMA statewide since Wednesday. “It’s a process, a long, arduous process,” said William L. McDaniel Jr., a Collier County commissioner. “But it can’t come quick enough.”

In East Texas, a FEMA mobile disaster center was scheduled to assist flooded residents one day last month in a courthouse parking lot in the town of Orange. “FEMA didn’t show up that day,” said Stephen Brint Carlton, a Republican who is the county judge and the top elected official in Orange County. “They don’t show up and we have a bunch of elderly people sitting out in a parking lot, and no one’s there to help them.”