New York and New Jersey officials are pushing the White House to seek $80 billion in Hurricane Sandy disaster aid, a hefty price tag that could spark opposition from conservatives.

New York Mayor Michael R. Bloomberg visited Capitol Hill on Wednesday, lobbying leaders and appropriators in both parties and chambers for roughly $42 billion for the metropolitan region. Separately, New Jersey Gov. Chris Christie released a statement Wednesday that said about $37 billion in federal aid would be needed for the Garden State. The spending would go toward the immediate costs of the response to the hurricane handled by the Federal Emergency Management Agency, as well as proposed longer-term projects to repair damaged infrastructure, hospitals, schools and businesses that would be addressed by other government programs.

The White House is weighing those requests but has yet to settle on a figure. The size and timing of an aid package could be complicated by ongoing negotiations between the administration and lawmakers over taming the federal deficit with steep spending cuts under consideration.

Charles E. Schumer of New York, the No. 3 Senate Democrat, said at a news conference on Wednesday that the Office of Management and Budget could send the official request to Congress next week. He said several aid packages may be needed.

The OMB is taking longer with the request than some lawmakers and aides had expected; some had hoped to see it this week. “We want to be careful. We want to do this right,” Schumer said

Schumer rejected the idea that, with more than $5 billion still remaining in the Federal Emergency Management Agency’s Disaster Relief Fund, there is no great urgency to move a disaster package. He said that money is being spent out very quickly from the fund.

The White House has said that more than $1.9 billion already has been obligated in connection with Sandy, including more than $960 million approved in direct assistance to hundreds of thousands of people who suffered losses in the storm.

GOP leaders have declined to offer much comment on the package before seeing a detailed White House proposal.

“We will consider the administration’s request, when they make one,” said Michael Steel, a spokesman for Speaker John A. Boehner of Ohio.

Some Republicans, including appropriators Jeff Flake of Arizona and Tom Latham of Iowa, already have said that other spending cuts would be needed to offset the disaster aid package in the House. The larger the initial package, the greater is the likelihood of a serious battle over spending offsets.

Schumer conceded backers of the aid package will face a “hard fight.” He added, “we are in the middle of very strenuous negotiations over the fiscal cliff, and we know that money is short in Washington.”

Bloomberg appealed to lawmakers to clear the aid package without seeking cuts elsewhere. He met with several Republicans, including House Majority Leader Eric Cantor of Virginia, who in the past advocated offsetting some disaster aid with spending cuts. While Bloomberg said that he was “comfortable” that lawmakers understood the need for rapid action, he didn’t get a “firm commitment” that Republicans wouldn’t seek offsets.

“Cantor has to listen to his colleagues and to his constituents, and listen to all of their arguments. He has got to look at the numbers that we have submitted to ascertain in his mind that they are legit,” Bloomberg said. “I think it would be irresponsible for him to, before he sees all the data, make a commitment.”

Bloomberg said that he and Cantor have “established a dialogue” about the aid request. “If he has questions, he won’t be reticent to pick up the phone,” he said.

Cantor declined comment on his plans for a supplemental spending measure after his session with Bloomberg. “The mayor’s doing well,” Cantor said simply.

Bloomberg also was expected to meet with Minority Leader Nancy Pelosi of California; Senate Majority Leader Harry Reid, D-Nev.; Senate Minority Leader Mitch McConnell, R-Ky., House Appropriations Chairman Harold Rogers, R-Ky.; and senior Senate GOP appropriators Susan Collins of Maine and Lamar Alexander of Tennessee.

Schumer and fellow Democratic senators Kirsten Gillibrand of New York, and Robert Menendez and Frank R. Lautenberg, both of New Jersey, were due to meet Wednesday evening with Jeffrey Zients, the acting director of the Office of Management and Budget.