Congress approved an initial $10.5 billion for relief funds last week.
The bulk of the latest $51.8 billion bill will go to the Federal Emergency Management Agency for shelter, food and medical care.
FEMA has faced harsh bipartisan criticism for lack of preparedness for Hurricane Katrina and ensuing flooding of New Orleans and other Gulf coastal areas.
"There was a system-wide failure," said Senate Majority Leader Bill Frist of Tennessee after Republicans met with President Bush at the White House, according to the Associated Press. He said there were problems at the local, state and federal levels and "we will get to the bottom of that" in a bipartisan congressional investigation.
Democratic leader Harry Reid of Nevada dismissed the idea of such a probe, saying that allowing Republicans to judge the performance of the Republican administration would be like having a baseball pitcher "call his own balls and strikes," reported the AP.
FEMA has spent an average of $2 billion a day in the storm's aftermath, mostly on the construction of temporary housing. The agency also plans to supply hurricane victims with $2,000 debit cards for food, gasoline and transportation.
About $1.4 billion of the aid package would go to the Defense Department for costs of personnel deployment and repair of facilities in the Gulf region, and $400 million would go to the Army Corps of Engineers for levee, pump and channel repairs in Louisiana bayou area.
Despite the enormous amount of the relief funding -- nearly $40 billion more than was spent all of last year on four hurricanes that pounded Florida -- the White House has made clear much more money will be needed.
"This will not be the last request," White House budget director Joshua Bolton told the Washington Post. This week's funding allocation, he told the New York Times, would "last at least the next several weeks."