By Rachel Witkowski and Leslie Scism 

Hurricane Harvey poses new hazards to a giant U.S. flood insurer already facing mounting debt and a reauthorization fight in Congress.

The National Flood Insurance Program, created about 50 years ago because private insurers were unwilling to risk catastrophic flood losses, could be inundated with billions of new claims following Harvey's initial Category 4 winds and colossal rainfall.

Yet the U.S. program is scheduled to expire on Sept. 30 and has just $5.8 billion left it can borrow from the Treasury to meet new claims, according to January figures reported to Congress. Many people buy the government policies through private-sector insurers, which are compensated for that service.

Members of Congress are discussing a number of options, ranging from a temporary renewal of the program to a more-comprehensive fix designed to return the program to solvency. Congress returns from recess on Sept. 5.

"From a public-policy perspective, Hurricane Harvey reinforces the narrative of why the national flood-insurance program is so important and needs to be addressed," said Christopher Gillott, legislative director of Sen. Bill Cassidy (R., La.).

What makes the debate in Washington, D.C. so challenging is that the program already has a debt of roughly $25 billion from earlier weather disasters. Much of that is from Hurricane Katrina in 2005 and superstorm Sandy in 2012. Sandy alone cost $8.4 billion initially, according to the Federal Emergency Management Agency, which manages the program.

The program had to borrow another $1.6 billion from the Treasury in January just to pay interest on its debt and storm claims, according to FEMA.

It will take days, if not weeks or longer, for claims to emerge from Hurricane Harvey. More than 200,000 homes along the Texas coast could be at risk, according to information and analytics firm CoreLogic. In 30 Texas counties labeled disaster areas by the state's governor there are nearly 450,000 NFIP policies covering $125.7 billion in insured value, according to the program's website. More than half of that value is in heavily populated Harris County, which includes Houston.

Previous interruptions of the flood-insurance program have triggered delays in thousands of home sales during the lapses.

Sticking points in Congress include whether lawmakers will address the federal program's finances in part by increasing rates gradually for homeowners who currently pay well below the actuarial risk of flooding.

Program critics have said many policyholders are getting bargain rates compared with what private-sector insurers would require and that taxpayers in drier parts of the country are subsidizing those in flood-prone states.

Roughly a dozen senators are proposing legislation that would adjust homeowners' rates to be more in line with a property's risk, and create incentives for private insurers to take on more policies. But that package, led by Sen. Bob Menendez (D., N.J.), is unlikely to pass next month since Congress would have only a few weeks to address it, according to Senate staff members.

The two top leaders of the Senate Banking Committee recently introduced a separate, simpler bill: It would renew the program for six years without getting into the more controversial financial woes. Lawmakers are also now discussing a shorter renewal period to extend the program to December, according to Senate staff members.

"A short-term extension will at least give us an opportunity to address the program sooner rather than doing a longer-term extension that would kick the can down the road," said Jason Tuber, senior adviser to Mr. Menendez.

More-traditional home insurers are increasingly willing to take on flood exposure instead of leaving that risk to the federal government -- thanks to improved flood models, satellite imagery and other tools.

"We developed a comfort level in underwriting it," said Matthew Power, a senior executive at American International Group Inc., among the private-sector carriers with an alternative to the federal policies.

But the private-sector market isn't big enough to fill the gap if the U.S. government were to let the federal insurance program lapse. AIG for now has about 20,000 flood-insurance policyholders nationwide. The U.S. program, by comparison, has roughly 5 million policyholders.

Craig Poulton, chief executive of Poulton Associates, which administers a private flood-insurance program, estimates that private primary flood insurance represents about 2% of the market.

Imagery of Harvey's flooding will show "that there needs to be [a federal program] to assist both individuals and businesses to rebound from flooding and severe storm damage," said Elizabeth Guimaraes, who chairs an external-affairs committee for the Risk and Insurance Management Society and is director of risk management at Nova Southeastern University in Florida.

Nicole Friedman contributed to this article.