Lawmakers are pushing a $1 billion aid package for the Federal Emergency Management Agency in the wake of the deadly Joplin, Mo., tornado — even as the agency is already stretched thin by other twisters and floods one week before hurricane season begins.

FEMA has already deployed more than 4,300 workers this year in response to dozens of federally declared disasters and has distributed about $149 million in aid. But it is carrying more than $17 billion in debt from storm-related aid in the past six years.

On Tuesday, the House Appropriations Committee approved $1 billion in additional disaster relief for FEMA as part of a measure funding the Department of Homeland Security for fiscal 2012. FEMA would use the money for the final four months of fiscal 2011.

Rep. Robert B. Aderholt (R-Ala.), whose state is reeling from deadly tornadoes last month, said his measure would provide enough short-term aid for the Joplin storm, historic Mississippi River flooding and the coming hurricane season.

“We just want to make sure that [FEMA is] not running real low by the end of the fiscal year,” he said Tuesday.

House Republicans, who require spending cuts whenever new spending is proposed, said the FEMA funds would be paid by cutting $1.5 billion from an Energy Department loan program for the production of fuel-efficient vehicles. Aides said the measure would probably pass the House next week.

Senate Majority Leader Harry M. Reid (D-Nev.) signaled support for the disaster aid, noting that “any time we have a natural disaster, we take care of the people.”

A White House budget spokeswoman said administration officials are closely monitoring the bill and will consider it if necessary.

President Obama, who campaigned on a promise of avoiding Hurricane Katrina-style mistakes, said he plans to visit Joplin on Sunday after a weeklong European visit.

“The American people are by your side,” Obama told storm survivors early Tuesday from London. “We’re going to stay there until every home is repaired, until every neighborhood is rebuilt, until every business is back on its feet.”

Aides said the president received multiple briefings on the tornado response Tuesday.

The death toll in Joplin surpassed 120 people Tuesday, making it the deadliest single U.S. tornado in six decades. The National Weather Service labeled the twister an EF5, the highest level possible, with winds greater than 200 mph. Forecasters said another tornado outbreak could pummel the Midwest on Wednesday.

Emergency officials are shifting the search for victims to flattened big-box retail stores and apartment complexes, said FEMA Administrator W. Craig Fugate.

“It’s another one of these very powerful tornadoes, where there’s not a lot of little damage,” he said. “It’s either you were destroyed or you got spared.”

Fugate, a former Florida state emergency manager, regularly instructs his agency to “go big, go fast, go hard” and spare no expense in the early days of a federal disaster response.

“The quicker you get in and get stabilized, the lower the cost will be long term,” Fugate said Tuesday from Joplin. “Until you get a community stable, you’ve got to go hard. Once you get to that point of stabilization you can shift gears and pull back.”

Fugate rebuffed overtures by the George W. Bush administration to lead FEMA in the years after Katrina, but once Obama tapped him in 2009, he ceded more operational control to regional administrators and is deploying personnel and equipment before storms. Agency officials in the field are instructed to take their cues from state and local leaders, who Fugate said better understand the needs of their communities.

FEMA also continues to pay victims of the Mississippi River floods through the National Flood Insurance Program. As of March 31 — the date from which the most recent records are available — FEMA had paid out $19.1 million in flood aid, with record claims expected in the coming weeks.

The NFIP collects more than $3 billion in insurance premium payments annually, but Fugate told senators last month that it could collect an additional $1.5 billion annually if not for the subsidized nature of the program. Since 2005, the agency said it has borrowed $17.75 billion from the U.S. Treasury to pay flood insurance claims, mostly for victims of hurricanes Katrina and Rita. It is unlikely to repay the debt, Fugate warned.

Though Congress normally forgives FEMA’s disaster-related debts, several congressional aides said no one is currently considering such action.

Fugate said total costs for this year’s natural disasters won’t be known for several more months, because affected towns and communities have yet to assess their rebuilding costs.

But he said in the short term, “the cash flow is still sufficient to support operations.”

Staff writers Paul Kane and Felicia Sonmez contributed to this report.