The damage from Hurricane Irene is still being tallied, and wildfires are spreading across Texas. But Congress signaled Tuesday that it still cannot agree on how to get more money into the nearly depleted coffers of the beleaguered Federal Emergency Management Agency.

Lawmakers are stuck in a dispute over how much additional funding FEMA should receive and whether that additional funding should be offset with cuts elsewhere.

Democratic senators on Tuesday proposed spending $6 billion to replenish the Disaster Relief Fund, the leading program used to reimburse local governments and individuals for disaster-related cleanup and repairs.

That’s $2.35 billion more than the GOP-held House included in a competing appropriations measure that passed in June.

That disparity feeds into the broader debate over whether the government can afford to boost spending on disasters without offsetting the funds with spending cuts elsewhere.

The House’s $3.65 billion for disaster relief eclipsed a springtime request from President Obama but was paired with matching cuts to other areas of FEMA and the scaling back of a program that provides loans to automakers that build energy-efficient cars.

Republicans said the cuts were necessary to prevent disaster relief from adding to the budget deficit.

But with Irene’s devastation looming large, Democrats have sensed a political opening and have been quick to criticize the GOP position.

“It’s irresponsible to cut the precise programs that help us prepare for and respond to future disasters in order to pay for past disasters,” said Sen. Mary Landrieu (La.), who chairs the Senate Appropriations homeland security subcommittee.

Both sides have insisted that disaster victims will receive the support they need to rebuild, but they have not found a compromise on the issue.

House Republicans say it is unfair to suggest that they are holding disaster relief hostage to spending cuts.

In fact, they note, the House’s measure dealing with the issue passed months ago and significantly enhanced the White House’s original $1.8 billion request for disaster funding.

“Nobody’s holding anything up,” House Majority Leader Eric Cantor told reporters after an event last week in his Virginia district, which was hit hard by Irene. “In fact, it’s the Senate that’s holding the bill up. They’re the ones who haven’t acted. We’ve acted in the House.”

But he insisted that it is “the responsible thing to do” to pay for the relief by cutting spending elsewhere.

It is a sign of the broader gridlock that has infected Washington that providing aid for disaster victims, once considered a bipartisan feel-good spending item, has become only the latest political football between the parties.

Congress returns to work this week still stymied over a series of issues that stalled it this summer during the bitter debate over raising the nation’s debt ceiling.

Lawmakers will clash in coming weeks over job-creation proposals that President Obama will announce in a speech to a joint session of Congress on Thursday evening and how a bipartisan committee created in the debt-limit deal should approach its task of cutting the deficit.

But a big goal for September is finding compromise on 12 spending measures to fund the government in the new fiscal year.

The Senate began Tuesday with a subcommittee meeting to consider funding for homeland security agencies, including the Disaster Relief Fund.

Stressed by a string of tornadoes, fires and floods, the fund has dipped to $566 million in recent weeks. Beyond the draft proposal intended to cover needs for the next year, Landrieu suggested that even more money might be needed just to get FEMA through the end of the month.

The funding would exceed limits imposed on discretionary spending under the debt deal agreed to in early August. But the deal allowed for some additional emergency disaster spending, and Democrats say the FEMA funding should qualify.

On Monday, the White House said it anticipates that the federal government will need to spend $1.5 billion to help communities recover from Irene, a figure that came on top of $5.2 billion in backlogged needs that the administration said have resulted from previous disasters.

But the White House has not submitted a formal request to Congress for additional funding.