New York Gov. Mario M. Cuomo said yesterday that one reason President Reagan won reelection so overwhelmingly last November is that voters never understood how serious a problem the federal budget deficit is, and Cuomo predicted that if Reagan is wrong in his belief that economic growth will eliminate the deficit, the Democrats will regain the White House next time around.

"If the president is wrong and the deficit is a problem, the Democrats will have a win -- with the AFL-CIO, without the AFL-CIO, with a man, with a woman, with a black, without a black -- if the Democrats have a good idea that sounds like it's going to work and a candidate who is a leader, they'll win," he said.

In a speech and question-and-answer session before the American Society of Newspaper Editors at the Sheraton Park Hotel, Cuomo, a leading possible candidate for the 1988 Democratic presidential nomination, offered a deadpan description of himself as "a governor who aspires to nothing more."

As laughter spread through the audience, Cuomo quipped: "I see there are no cynics in this room."

He predicted that Reagan eventually will be unable to escape the need for raising taxes to reduce the deficit.

"You saw the president withdraw from his commitment on defense; you saw him withdraw on Social Security," Cuomo said, referring to the budget compromise Reagan worked out last week with Republican senators, which called for smaller increases in defense spending and Social Security cost-of-living adjustments than he promised in his campaign. "Are taxes any more important than defense? Are taxes more sacred than the commitment to the elderly?" Cuomo said.

Cuomo said government works well when "the people are informed and help make policy"; he questioned how the electorate can be informed in the age of television, "with a 28-second debate on the death penalty and 30 seconds for 'Star Wars.' "

He said Reagan won in November because of his personal popularity, the "apparent economic recovery" and the fact that the country was at peace; he added that Democratic nominee Walter F. Mondale blundered early in the campaign by proposing a tax increase.

"In the long run, he may be proved correct, however," Cuomo said. "No one understood the deficit because people were home raising two kids or running a business. The budget deficit hasn't made it into your living room, into your college budget -- yet."

Cuomo predicted that Reagan will reverse his position on a tax increase by claiming an overwhelming mandate for it. He said the president will describe such an increase as something else, such as "tax simplification," and further predicted that income tax rates for lower- and middle-income taxpayers will not be reduced as much as has been promised.

"There are ways to generate revenue, such as raising the minimum corporate tax, without taxing people oppressively," the governor said.

Cuomo decried Democrats who argue that the party has to cut loose from its past and head in a new direction.

"We should not say we need a whole new philosophy, since the one we have is good enough for Reagan," he said to laughter. "Last year he never mentioned Eisenhower or Nixon or Ford, but he invoked Truman and Roosevelt and Kennedy -- over and over. He won that way. Why should we give up Truman and Roosevelt and Kennedy?"

He told the editors that freedom of the press under the First Amendment was intended by the Founding Fathers as "a fundamental right" and a "protection against government's instinct for oppression."