The House vote took place five days after the White House requested about $7.9 billion in emergency aid. The vast majority of that money would go to the Federal Emergency Management Agency, and $450 million would go to the Small Business Administration’s disaster loan program. And with Hurricane Irma barreling toward Puerto Rico and Florida, more disaster aid is likely to be needed quickly.

“Help is on the way,” said Representative John Culberson, Republican of Texas.

The Senate majority leader, Mitch McConnell of Kentucky, has voiced support for a speedy vote to approve the disaster aid in that chamber. But looming over the House vote was an emerging plan in the Senate to link an increase in the debt limit to the hurricane measure — a move that may still lead to a showdown with House conservatives.


A trailer park in Beaumont, Tex., that flooded during Hurricane Harvey. Conservatives must grapple with whether to support the Harvey aid measure even though the House bill does not include spending cuts to pay for it.

Andrew Burton for The New York Times

The Treasury secretary, Steven Mnuchin, has urged Congress to raise the debt limit by Sept. 29. He said in an interview on “Fox News Sunday” that he and President Trump wanted the debt limit measure to be tied to the Harvey aid, warning that failing to raise the borrowing limit could imperil getting aid to Texas.

Speaking Tuesday on the Senate floor as Congress returned from its summer recess, Mr. McConnell embraced that argument, quoting from Mr. Mnuchin’s interview. The No. 2 Senate Republican, John Cornyn of Texas, told reporters that Mr. McConnell had decided to attach the debt limit increase to the Harvey measure.

The Senate Democratic leader, Chuck Schumer of New York, and the House Democratic leader, Nancy Pelosi of California, supported a three-month increase along with the hurricane aid to give Democrats leverage later this year when other matters, including a longer-term government funding deal, could be negotiated between the two parties.

Mr. Ryan responded by saying the Democrats’ proposal was “unworkable, and it could put in jeopardy the kind of hurricane response we need to have.”

“To play politics with the debt ceiling, like Schumer and Pelosi apparently are doing, I don’t think is a good idea,” Mr. Ryan said.

Aside from the particulars of a debt-limit increase, just the idea of raising the government’s borrowing capacity in tandem with providing Harvey aid is drawing opposition from conservatives, who have pushed for any debt limit measure to be coupled with fiscal changes intended to rein in spending.

“Attaching the debt ceiling to it is using a catastrophe in Texas as leverage to pass something that certainly there should have been an alternative plan to pass,” said Representative Mark Meadows, Republican of North Carolina and the chairman of the House Freedom Caucus.


John Cornyn of Texas, the No. 2 Senate Republican, on Tuesday in Washington. He told reporters that Senator Mitch McConnell, the majority leader, had decided to attach the debt limit increase to the Harvey measure.

Pete Marovich for The New York Times

Representative Mark Walker of North Carolina, the chairman of the conservative Republican Study Committee, expressed frustration at what he views as a missed opportunity to address the nation’s debt.

“We’re grateful that in Texas the floodwaters continue to recede,” he said on Fox News. “But here in the swamp, it looks like they continue to rise.”

Dan Holler, a spokesman for Heritage Action for America, a conservative group, said the White House and congressional leaders were putting conservative lawmakers — including those from Texas — “in a pretty difficult political situation” by essentially daring them to vote against a measure containing both Harvey aid and an increase to the debt limit.

“Linking those two things together is not something that any conservative wants,” Mr. Holler said. But, he added, “there doesn’t seem to be a will in Congress or in the administration at this point to tackle some of those major drivers of our debt and deficit problem.”

Conservatives must also grapple with whether to support the Harvey aid even though the House bill does not include spending cuts to pay for it. The Club for Growth, a conservative group, had urged House members to vote against the Harvey bill if it was not fully offset by spending cuts, and the group also objected to the prospect of linking the debt limit to the hurricane aid.

“A debt ceiling increase is nothing more than Congress bailing itself out — at taxpayer expense — because Congress routinely fails to balance the budget,” the group wrote. “So adding the debt ceiling increase to the disaster relief bill is just throwing bad policy on top of bad policy.”

Asked if he worried about a backlash from conservatives, Mr. Cornyn told reporters, “None of this is easy, so I guess the answer is no.”

Even before the hurricane, lawmakers already faced a challenging September, with a host of time-sensitive issues that must be resolved. Among other things, lawmakers need to provide funds for the Children’s Health Insurance Program, and they need to reauthorize the National Flood Insurance Program and the Federal Aviation Administration.

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