President Reagan and Reaganomics hovered over New York's gubernatorial race today like giant balloons in Macy's Thanksgiving parade, hoisted repeatedly by liberal Democrat Mario Cuomo faster than conservative Republican Lewis Lehrman could cut the supply-side ties that now bind him.

"My opponent says Reaganomics has not gone far enough," Cuomo said today at the start of their first debate in a race that may become the nation's foremost referendum on the president and his economic policies.

"So far it has cost the state approximately $2 billion, created a Depression-like unemployment rate, destroyed thousands of small businesses."

Lehrman, a supply-side disciple who once campaigned privately to become Reagan's treasury secretary and advised him on economic policy, now is in the politically uncertain position of campaigning publicly in defense of it. Lehrman is seeking to adapt the national supply-side philosophy to statewide purposes, proposing a 40 percent cut in state income taxes and a halving of state sales taxes over eight years.

"It wasn't President Reagan who drove 7,000 people out of the State of New York in the 1970s," said Lehrman. " . . . It wasn't President Reagan who made New York State an economic backwater . . . in the late 1970s."

So it went in this contest where Cuomo now holds a relatively narrow lead in the polls with less than a month to go. From time to time, the candidates strayed into such statewide issues as welfare and mental health and crime. But eventually Cuomo led them back to Reaganomics.

"Never in the history of this nation has an economist been more incorrect than you were when you suggested to Ronald Reagan that the way to save this nation was to give back $250 million in taxes," Cuomo said. "We now face the greatest unemployment since the Depression, bankruptcies everywhere, a proliferation of despair."

To which Lehrman, whose taut debating style and short fuse frequently worry his advisers and supporters, responded with humor. First he quoted the outraged declaration of an Irish politician that "Half of the lies my opponent tells about me are not true!"

Then he delivered a brief defense of the supply-side advice he gave to president-elect Reagan.

"I have had my differences with President Reagan," Lehrman said, striving to put some difference between himself and his party leader. " . . . The program I recommended -- a balanced budget, a sound and honest dollar, a stable currency, and a cutback and weeding-out of unwise expenditures in the Pentagon -- was a policy which in part he followed and in part he rejected."

This is, in fact, what the record shows in two memos Lehrman wrote in late 1980, stamped "confidential," and sent to the Reagan transition team.

"President Reagan should pledge to balance the budget in 1983 -- not 1984 -- and to establish a gold standard," Lehrman wrote. "Then he should cut, and cut drastically, military spending for the great powers abroad who are shirking their duty. He would then announce the future refinancing of the entire national debt.

"These are drastic measures, but we need drastic measures."

Elaborating on his views on the gold standard, Lehrman also wrote: "Since . . . President Nixon destroyed the last link between the dollar and gold, we have had a purely paper currency. Anyone who has ever visited the Bureau of Engraving and Printing in Washington, and watched its speedy German presses spew out paper dollars, knows engraved paper is not wealth. Economic value comes only from hard work, and hard work must be paid in hard money."

In explaining his views on defense spending, Lehrman wrote: "The defense budget must actually be cut. Military spending is, of course, necessary . . . but from a peaceful economic standpoint, military spending takes real resources and technical ability, and blows them out of cannon into nothingness. War and the preparation for war destroy wealth . . . ."

According to the latest polls of both candidates, Cuomo has a lead of about five to seven points over Lehrman. A statewide poll by Newsday, the Long Island newspaper, published today shows the race even closer: Cuomo 43, Lehrman 41, with 16 percent undecided.

The Newsday poll showed Cuomo dominating the city vote, 62 to 23, with Lehrman carrying upstate 51 to 33 and leading in the suburbs by a relatively close 47 to 38.

Lehrman strives to solidify that suburban and conservative vote by portraying himself in often harsh rhetoric as the toughest law-and-order candidate.

Cuomo opposes the death penalty. Lehrman champions it, declaring today: "Life is so precious. . . it is because life is unique and God-given that in Genesis and Leviticus this penalty is authorized."

Lehrman's greatest concern remains, however, the intrusion of national policy into the statewide race. Just before the debate, Lehrman's campaign manager, Karl Ottosen, was asked how he believed Reaganomics would affect the contest. "We'll defuse it," he replied.

Today, Cuomo sought outside assistance in his effort to keep the issue alive. After successfully turning the debate toward Reaganomics one more time, Cuomo said to Lehrman:

"President Reagan said he would come here and campaign for you, but he hasn't been asked. I'm asking him--to come here, and campaign for you."