Stung by criticism of the federal response to Hurricane Katrina, President Bush yesterday promised to investigate his own administration's emergency management, then readied a request for tens of billions of dollars for relief and cleanup.

From the Pentagon to Capitol Hill, official Washington spent yesterday grappling with a hurricane recovery effort that, according to some estimates, will cost more than $100 billion and influence a broad range of federal policy, from emergency response to coastal development, from expanded domestic oil exploration to the future of the estate tax.

Bush vowed to "find out what went right and what went wrong." Defense Secretary Donald H. Rumsfeld said that the military already has begun a "lessons-learned" assessment of its coordination with state and local governments. Nine Cabinet members briefed Senate and House leaders last night on the federal response, and key senators pushed for changes that would allow Third World relief efforts to be emulated in the United States.

"Nothing will be the same again," said Sen. Trent Lott (R-Miss.), whose Pascagoula home was destroyed.

Just days after Congress approved a $10.5 billion emergency relief package, Bush informed congressional leaders of a request of as much as $40 billion, making Katrina the federal government's most expensive domestic emergency ever. The package could be passed as early as today, aides said.

But with the Federal Emergency Management Agency spending more than $500 million a day, lawmakers from both parties said the cost will climb much higher. Senate Minority Leader Harry M. Reid (D-Nev.) suggested the total could exceed $150 billion, with $100 billion for FEMA alone. Lott said the cost will be "well in excess of $100 billion," and few were disagreeing.

Beyond money, congressional leaders ordered committee chairmen to draft any legislation that could remedy the problems revealed by the hurricane and its aftermath. And after nearly a week of recriminations, Washington slipped into an extraordinary bout of self-reflection.

"It is fair to say the overall response to this emergency could have and should have been better," House Majority Leader Tom DeLay (R-Tex.) said.

Sen. Barbara A. Mikulski (D-Md.) called for FEMA Director Michael D. Brown to leave and be replaced by "an experienced, professional emergency manager."

Speaking to reporters after a Cabinet meeting , Bush said: "It's very important for us to understand the relationship between the federal government, the state government and the local government when it comes to a major catastrophe. . . . We want to make sure that we can respond properly if there's a WMD [weapons of mass destruction] attack or another major storm."

Bush, who has called the response to the hurricane unacceptable only to amend that to say the results were not acceptable, offered no specifics on his planned investigation. Still, the call for an investigation was unusual coming from a president who rarely admits mistakes.

House Republican leaders suggested that Congress launch one comprehensive examination of the disaster response, possibly a joint House-Senate investigation. But Senate committees were already moving forward. The Senate Homeland Security and Government Affairs Committee has scheduled hearings next week to examine the federal disaster response.

Sen. James M. Inhofe (R-Okla.), chairman of the Senate Environment and Public Works Committee, promised his own examination of Gulf Coast infrastructure, water projects and coastal erosion. Next week, the panel will look into Katrina's impact on energy supplies, a subject examined yesterday by the Senate Energy and Natural Resources Committee and set to be examined today by the House Energy and Commerce Committee.

At the Senate Energy Committee hearing, Sen. Pete V. Domenici (R-N.M.) said Congress must accept politically difficult measures that lawmakers have repeated rejected, such as raising car and truck fuel efficiency standards.

House Minority Leader Nancy Pelosi (D-Calif.) castigated the Cabinet's performance as two hours of "self-congratulatory" talk. "This administration does not live in reality," Pelosi said. "To hear them talk, everything went right. . . . They have very low standards, and no performance, and no accountability."

DeLay said the GOP leadership was working to bring legislation to the floor, possibly this week, that would loosen rules that govern federal assistance programs. He chastised Rep. Thomas M. Davis III (R-Va.) for seeking to open hearings next week on the response.

Senate Finance Committee Chairman Charles E. Grassley (R-Iowa) proposed retooling a resettlement program for foreign refugees to help Americans displaced by Katrina.

But there was little immediate agreement on how to proceed and many notes of discord.

House and Senate lawmakers said they will proceed with a package of $70 billion in tax cuts and $35 billion in entitlement spending cuts, including as much as $10 billion out of a Medicaid program they simultaneously were suggesting expanding.

Before Katrina struck, the House and Senate were at loggerheads over an energy and water spending plan for the fiscal year that begins in October, with the Senate hoping to spend $700 million more than the House on water projects, including $27 million more on flood control in southeastern Louisiana and $20 million more on Louisiana coastal protection. House Appropriations Committee spokesman John Scofield said the committee has received no instructions to budge: "We are committed to living within our budget."

With federal resources stretched, Grassley questioned a rush to temporarily lift the tax on airline fuel, and he lambasted proposals to offer more tax incentives to oil companies for domestic oil exploration. "With $60 [a barrel] oil, you don't need more incentives," he said. "What we need is for the oil companies to take some of their profits and lower the cost of gasoline."

DeLay had a similar response to suggestions that the federal gasoline tax be suspended: "Now more than ever you're going to need . . . those highway trust funds, to rebuild the bridges that were destroyed, rebuild the railroads that were destroyed."

At the Pentagon, Rumsfeld said the involvement of troops in hurricane relief efforts will not diminish the military's ability to sustain operations in Iraq and Afghanistan.

He noted that more than 300,000 Army National Guard and Air National Guard troops remain available to help. He sharply rejected the suggestion that the commitment of large numbers of troops to Iraq -- including National Guard soldiers from Louisiana and Mississippi -- had delayed the military's response. About 41,000 Guard troops are in assisting the region.

"Not only was there no delay," said Gen. Richard B. Myers, chairman of the Joint Chiefs of Staff. "I think we anticipated in most cases -- not in all cases, but in most cases -- the support that was required."

Staff writers Bradley Graham, Amy Goldstein, Shailagh Murray and Spencer S. Hsu contributed to this report.