WASHINGTON – Andrew M. Cuomo, traveling to the nation’s capital for the first time as governor of New York, said after a round of Capitol Hill meetings Monday that he’s optimistic that the state will get the federal aid it needs to rebuild in the wake of Superstorm Sandy – but a key question about prospects for that aid remains unanswered.

Will the Republican-controlled House approve the aid in the midst of “fiscal cliff” talks, without the promise of the same amount in federal budget cuts elsewhere?

After meeting with White House officials and congressional leaders, Cuomo held a briefing for the state’s congressional delegation and said: “All the meetings we had today were positive. People really understand the scope of the damage.”

Perhaps most important, Cuomo said, he had a good meeting with House Speaker John A. Boehner, R-Ohio, who presides over a GOP-controlled House that has been increasingly reluctant to fund disaster relief that isn’t offset by budget cuts elsewhere.

“He said he wants to be helpful,” Cuomo said of Boehner. “He wants to be there for New York. It’s fair to say he was optimistic.”

Yet when asked whether the House would pass a Sandy aid package without offsetting budget cuts – which would make it easier to put the legislation together – he said: “We did not have that specific a conversation.”

More than a month after Sandy ravaged New York City, Long Island, New Jersey and other parts of the Atlantic Coast, White House officials are putting together an aid request that, Cuomo said, could be sent to Congress next week, with hopes that it will pass by the end of the year.

New York State alone is asking for $42 billion in aid, with $9 billion of that total devoted to protection from future storms. Meanwhile, New Jersey Gov. Chris Christie – a Republican who will make his own lobbying visit here later this week – has said storm damage in his state totals $36.8 billion.

Other governors have not yet submitted their requests, so it’s unclear how big such an aid package will be. Congressional aides presume that it will be huge, though New York is not likely to get every dime it is seeking.

The state will have to justify its request, Rep. Tom Reed, R-Corning, said, while vowing his support for the package.

“You know there’s been a cultural shift” toward questioning additional federal spending, Reed said in a conference call with reporters before Cuomo’s visit.

Like Cuomo, Reed said that he was optimistic that Congress would approve a major aid package but that the timing is tight, with the holidays approaching and Congress dealing with the looming “fiscal cliff” that would bring automatic tax increases and budget cuts as of Jan. 1.

Cuomo met with White House chief of staff Jack Lew; Housing and Urban Development Secretary Shaun Donovan; top senators on the Appropriations Committee; Senate Majority Leader Harry Reid, D-Nev.; House Minority Leader Nancy Pelosi, D-Calif; and Boehner.

His visit here came as the Siena Research Institute released a poll showing that two-thirds of state residents who responded said Cuomo had done either an excellent or good job after the storm. About 22 percent rated his performance fair, and 7 percent considered it poor.

President Obama and New York Mayor Michael R. Bloomberg also got high marks in the poll, which showed that 69 percent of respondents believe that recent storms are connected to global climate change.