Congress must decide by Dec. 8 whether to keep the program going. An unusual coalition of insurers, environmentalists and fiscal conservatives has joined the Trump administration in calling for fundamental changes in the program, including direct competition from private insurers. The fiscal conservatives note that the program was supposed to take the burden off taxpayers but has not, and environmentalists argue that it has become an enabler of construction on flood-prone coastlines, by charging premiums too low to reflect the true cost of building there.

The program has other troubles as well. It cannot force vulnerable households to buy insurance, even though they are required by law to have it. Its flood maps can’t keep up with new construction that can change an area’s flood risk. It has spent billions of dollars repairing houses that just flood again. Its records, for instance, show that a house in Spring, Tex., has been repaired 19 times, for a total of $912,732 — even though it is worth only $42,024.

And after really big floods, the program must rely on armies of subcontractors to determine payments, baffling and infuriating policyholders, like Mr. Clutter, who cannot figure out who is opposing their claims, or why.

Roy E. Wright, who has directed the flood insurance program for FEMA since June 2015, acknowledged in an interview on Friday that major changes were called for and said some were already in the works. The program’s rate-setting methods, for example, are 30 years old, he said, and new ones will be phased in over the next two years. But other changes — like cutting off coverage to homes that are repeatedly flooded — would require an act of Congress.