WASHINGTON — At last, the storm-racked Northeast is getting a House floor vote on billions in disaster relief aid for victims of October’s Superstorm Sandy, but only after a host of East Coast Republican lawmakers threatened a near mutiny against GOP Speaker John Boehner.

A $9.7 billion measure to pay flood insurance claims, which amounts to just a down payment on a multibillion-dollar aid commitment, is expected to be approved by the House on Friday, boosting prospects for relief for the many home and business owners devastated by the storm. If the House acts as expected, the Senate plans to follow with a likely uncontested vote later in the day.

The Federal Emergency Management Agency warns that the National Flood Insurance Program will run out of money next week if Congress doesn’t provide additional borrowing authority to pay out claims. Congress created the FEMA-run program in 1968 because few private insurers cover flood damage.

The flood insurance measure is the first phase of a proposed Sandy aid package. Under Boehner’s new schedule, the House will vote Jan. 15 on an additional $51 billion in recovery money. Senate action on that measure is expected the following week. Financially strapped local governments are awaiting that money.

Northeast lawmakers say the money is urgently needed for storm victims awaiting claim checks from the late October storm, which was one of the worst ever to strike the Northeast, ravaging the coast from North Carolina to Maine, with the most severe flooding occurring in Atlantic City, N.J., New York City and Long Island and along the Connecticut coastline.

“People are waiting to be paid,” said Rep. Frank LoBiondo, R-N.J., whose district includes Atlantic City and many other coastal communities hard hit by the storm. “They’re sleeping in rented rooms on cots somewhere, and they’re not happy. They want to get their lives back on track, and it’s cold outside. They see no prospect of relief.”

The Club For Growth, a conservative group, on Friday urged lawmakers to oppose the bill, saying that Congress should only approve Sandy aid in installments to make sure the money is wisely spent and that any new Sandy aid should be offset with spending cuts elsewhere.

“Congress should not allow the federal government to be involved in the flood insurance industry in the first place, let alone expand the national flood insurance program’s authority,” the group said in a statement.

Boehner, of Ohio, had promised a House vote on Friday after his decision to delay an action on a broader Sandy relief package provoked outrage from Northeast Republicans, including New Jersey Gov. Chris Christie, who said he’d lost trust in GOP leaders in Congress after being promised a vote earlier this week.

About 140,000 Sandy-related flood insurance claims have been filed, FEMA officials said, and there are about 115,000 pending claims. Many flood victims have only received partial payments on their claims.

Philip Rock has received $8,000 in flood insurance payments so far but said he is awaiting a statement on the final amount, which he expects to be much more. A house he owns in Toms River, N.J., had a $220,000 flood insurance policy. The house, which he rents out, was destroyed, and he needs to know the final payout before he can demolish it.

The house is a “total loss,” Rock said. “We don’t want to demolish the house and have them say, ‘We have to go around and take more pictures.”’

New York, New Jersey and Connecticut were the states hardest hit by the storm in terms of damage from high winds, flooding and storm surges. The storm damaged or destroyed more than 72,000 homes and businesses in New Jersey. In New York, 305,000 housing units were damaged or destroyed and more than 265,000 businesses were affected.

Speaking of the legislation pending Friday, Rep. Michael Grimm, R-N.Y., whose district includes Staten Island, said, “This funding will give the city and state the much-needed resources to rebuild our damaged infrastructure and provide further aid to individuals and small businesses struggling to pick up the pieces of their lives.”

Sandy was the most costly natural disaster since Hurricane Katrina in 2005 and was blamed for at least 120 deaths. Northeast lawmakers have complained that it took just 10 days for Congress to approve about $50 billion in aid for Katrina but that it hasn’t provided aid for Sandy relief in more than two months.

“States and local communities need to know the money will be there before they can give a green light to start rebuilding,” said LoBiondo.

More than $2 billion in federal money has been spent so far on relief efforts for 11 states and the District of Columbia struck by the storm. New York, New Jersey, Connecticut, West Virginia, Virginia, Maryland, New Hampshire, Delaware, Rhode Island, Pennsylvania, Massachusetts and the District of Columbia are receiving FEMA aid.