The hastily scheduled votes came in response to criticism from Republicans — notably New Jersey Gov. Chris Christie — who publicly complained that GOP leadership in the House of Representatives was dragging its feet on the aid package.
The flood program, created in 1968, is expected to run out of money in coming days, complicating insurance claims for thousands of families in New York, New Jersey and other states that were hit by the storm.
About 800 claims are pending from Maryland, according to the Federal Emergency Management Agency. The Eastern Shore, and Somerset County in particular, experienced damaging floods after the storm.
The bill is the first of two Congress will take up to address dwindling disaster relief funds. The House is expected to vote Jan. 15 on a more controversial measure that includes an additional $50 billion in aid. That legislation would guarantee additional aid for Maryland, though the precise amount would be determined later.
Christie, who leveled stinging criticism of his own party over the issue earlier in the week, released a joint statement Friday with New York Gov. Andrew M. Cuomo, calling the insurance bill a "necessary and critical first step" but "just a down payment" toward aiding their states.
The Senate passed a $60.4 billion aid package last month, though the bill faced criticism over proposed spending not directly related to Sandy.
Several lawmakers criticized the decision not to hold a vote on that bill on Jan. 1, after Congress wrapped up work on "fiscal cliff" legislation, raising taxes on high-income households to avert automatic tax increases and spending cuts.
"While it is never too late to do the right thing, it is late that we are doing this thing," Rep. Steny Hoyer of Southern Maryland, the second-highest-ranking Democrat in the House, said of the insurance bill. "We are doing only the bare minimum. … We should have acted almost immediately."
Rep. Andy Harris, who represents the Eastern Shore, was one of 67 Republicans to vote against the proposal. He said Thursday that he will not support the bill unless budget cuts are found to pay for the additional spending. In a statement Friday, he said the current flood program needs to be reformed.
"The bill increased the program's borrowing limit from $20.7 billion to $30 billion with no plan to pay for it, and included no plans to make sure we would not have to bail out the program again in the near future," Harris said.
In the House, all Democrats and 161 Republicans voted for the measure.
Maryland Democrats pounced on Harris' vote, calling it "shameful and outrageous" in a statement.
The flood legislation does not authorize direct spending; rather, it gives the flood insurance program authority to borrow money to pay claims during times of heavy flooding. In the past, those loans have been repaid with premiums property owners pay to carry the insurance.
For decades, the program has repaid the loans, but the fund went deeply into debt following Hurricane Katrina and now is nearly $18 billion in the red, according to the nonpartisan Congressional Research Service.
Still, the program is making payments on that debt, including $750 million in the first half of 2011 and $500 million in 2010.
Sandy, a hurricane before the center of the storm made landfall Oct. 29 in New Jersey, caused more than 125 deaths in the United States.
Tribune Newspapers' Washington bureau reporter Richard Simon contributed to this article.