The Senate approved a $60 billion measure for Sandy victims on Friday.
"We have a new Congress that gets sworn-in [Thursday]. We need to get this [Sandy] bill on the floor as the first order of business," Israel said on "Squawk Box."
While the House failed to vote on the Sandy bill, it did pass a deal to avoid the "fiscal cliff."
"I voted for this bill. There was plenty in this bill I didn't like," he said. "I wish we achieved more deficit reduction."
The cliff deal that passed by the House late Tuesday included a delay of the automatic spending cuts for two months and income tax increases for American families making more than $450,000 — a higher level than the $250,000 threshold President Barack Obama wanted. (Read More: US Avoids Calamity in 'Fiscal Cliff' Drama)
"I've been preaching for two years that $250,000 may make you rich in some areas of the country, but not in high cost of living areas like New York, New Jersey, California and elsewhere," pointed out Israel who's also chairman of The Democratic Congressional Campaign Committee (DCCC) — the official campaign arm of his party in the House of Representatives.
In the next 60 days or so, the president and Republicans are going to have to cut two deals: one on spending cuts and the other on whether to raise the nation's borrowing limit. Already, the president said he's not going to negotiate on the debt ceiling — a troubled road he went down with Republicans in 2011 that resulted in Standard & Poor's lowering the AAA credit rating of the U.S.
Israel fully supports the president on the debt limit. "We cannot play games with the full faith and credit of the United States government," he emphasized. "We can not play games with the debt ceiling."
—By CNBC's Matthew J. Belvedere; Follow him on Twitter @