Quick passage of a measure to fund the government past the end of the fiscal year on Sept. 30 could be derailed by a new fight between the House and Senate over disaster relief spending.

If not resolved, the clash could result in a government shutdown— exactly the kind of brinksmanship that both parties have pledged to work harder to avoid.

Having failed to come to agreement on a series of measures to fund government for the 2012 fiscal year, both chambers must now pass a stopgap measure before the month ends that would keep agencies running through Nov. 18.

That continuing resolution, which faces a House vote Wednesday, is designed to give the parties time to keep negotiating over spending for the remainder of the year.

Both sides are optimistic that the critical short-term bill will be approved because the big issue that had been dividing them — how much to spend in total — was already agreed to in the August compromise over raising the nation’s debt ceiling, in which Congress agreed to spend $1.043 trillion for the year.

At issue now are funds for the Federal Emergency Management Agency, where the relief fund that reimburses local governments and individuals for repairing disaster damage has almost run dry as a result of months of devastating storms, tornadoes and fires. As of Tuesday, the fund had dipped to $256 million.

Republicans in the House have included $774 million for the fund in their continuing resolution, money that would be made available immediately upon passage of the bill, as well as $226 million for flood relief efforts by the Army Corps of Engineers.

Their measure would also authorize $2.65 billion for the disaster relief fund for fiscal 2012.

They say the bill will ensure that dollars reach affected communities, and that they are willing to revisit the 2012 figure in future talks if more is needed.

“The House is going to act,” House Majority Leader Eric Cantor (R-Va.) told reporters Tuesday. “We’re going to deliver the money to the victims of the disasters.”

But Senate Democrats say the House is not spending nearly enough. The White House recently said the disaster relief fund needs $500 million immediately and will need $4.6 billion next year.

They also reject House GOP efforts to offset $1.5 billion of the funding with a cut to a program that offers loans to car companies to encourage the production of energy-efficient vehicles.

Ten Senate Republicans joined Democrats last week to approve their own $6.9 billion disaster relief measure that would fully fund Obama’s request, as well as $1.8 billion in additional disaster cleanup funds.

Emboldened by that legislative victory, Senate Majority Leader Harry M. Reid (D-Nev.) said Tuesday that he will try to amend the House’s measure with the Senate’s $6.9 billion figure when it arrives later this week.

House leaders say a bill with the higher FEMA funding cannot pass their conservative chamber.

House leaders will probably need some Democratic votes Wednesday to overcome opposition from conservative Republicans who would like to see the measure cut more in spending. House Minority Whip Steny H. Hoyer (D-Md.) said Tuesday that Democrats “will be loathe to support the measure” because of the offsetting cut to an auto program many believe creates jobs.

Senate Minority Leader Mitch McConnell (R-Ky.) downplayed the possibility of a shutdown.

“Congress always responds appropriately to disasters,” he told reporters. “We’re having a discussion about the appropriate way to do that, and I’m confident it’ll be resolved.”

But Reid said he was “not as certain.”

“We’re not going to cave in on this, because it’s a matter of principle,” he said.