New York's next governor -- a millionaire . . . or a Shakespeare buff?

It had already been a good day for New York State Lt. Gov. Mario M. Cuomo, the Democratic candidate for governor, and it was barely noon. Mr. Cuomo had breezed through an interview with William O'Shaughnessy, president of WVOX, a New Rochelle, N.Y., radio station, and the man who heads ''Republicans for Cuomo.''

Three polls showed him ahead of Republican challenger Lewis E. Lehrman, a millionaire businessman and political neophyte whose economic blueprint for the state, released the day before, had been branded a ''carbon copy'' of Reaganomics in many newspaper editorals appearing this morning.

A few days earlier, Lewis Lehrman, son of a grocer and grandson of a poor Russian immigrant, was equally hopeful and buoyant. Wearing gray slacks, a white shirt, and his trademark, bright red suspenders, he was about to doff his suit jacket and begin campaigning along the streets of Borough Park, a predominently conservative Jewish section of Brooklyn, with jaunty informality.

But other than the suspenders and the candidate's ready smile, there's nothing casual about the Lehrman campaign drive.

''This is the most scholarly campaign I've ever covered,'' said one veteran newsman about the Cuomo campaign. Cuomo's remarks to reporters, and even some of his speeches, are punctuated with quotes from Shakespeare. Mr. Lehrman, a graduate of Yale University, is not without his own allusions to such figures as Alexis de Tocqueville.

But any similarity of style between Lehrman and Cuomo ends there. For the most part, Lehrman's speechs are brief, his sentences compact and simple, spoken with little emotion. By contrast, Cuomo's speechs are often a study in complexity. Yet he often speaks ardently and passionately, like a lawyer defending a case in criminal court. And in fact he began his political career as a public defender.

''I'm afraid you can't package this particular candidate in 30 seconds,'' said New York Daily News columnist Jimmy Breslin, referring to Cuomo's reluctance to sum up his positions on various issues on television and out on the campaign trail.

Overall, for both the primary and general elections, Lehrman will outspend Cuomo by roughly 3 to 1 - or more than $10 million to about $3.5 million, according to campaign sources. Lehrman's political war chest is believed to be the largest of any candidate in the country running for statewide election this year, and even exceeds what the late Gov. Nelson A. Rockefeller spent during his last gubernatorial bid. Lehrman has applied the bulk of his funds toward TV spots. Since last spring, hundreds of Lehrman commercials have been shown from Buffalo to the Big Apple.

The ads have aired so frequently that the New Yorker magazine ran a cartoon showing a parrot next to a television set. The parrot says, ''I'm Lew Lehrman. Lew Lehrman for governor! . . .''

The barrage of television ads have effectively turned Lewis Lehrman into a household term. In his Borough Park, Brooklyn, campaign swing here recently, one youngster shouted, ''There's the man on TV!''

In the ads, as well as in person, Lehrman comes across as an affable, straightforward, well-meaning individual who wants to use his wide experience as a businessman for the public good. He is chairman of the board of the Rite-Aid Corporation, a health-and-beauty chain store.

Lehrman favors the death penalty as one means of reducing violent crime; Cuomo opposes it, citing studies saying the death penalty won't reduce crime. Cuomo's support for government-funded abortions angers anti-abortion advocates; Lehrman opposes the idea.

Lehrman esposes economic policies similiar to the proposals Ronald Reagan put forth in his 1980 presidential campaign. Officially, the White House says that Lehrman is doing so well he doesn't need the President to do any campaigning for him in New York State. Privately, Lehrman aides say that any appearance by Reagan in Lehrman's behalf would do more harm than good.

But as much as Cuomo tries to link Lehrman with Reaganomics, analysts point to a concern by many New York State voters that some of the state's economic woes - including some of the highest taxes in the nation - can be directly traced to overspending by state Democrats over the last two years of the administration of Gov. Hugh Carey and his lieutenant governor, Mario Cuomo.

If Lehrman's conservative economic policies are right of center, Cuomo's a bit to the left. Increasingly, Lehrman commercials paint Cuomo as an advocate of the ''tired old liberal ideas'' in an effort to woo Republicans and conservative Democrats.

Polls indicate that the state of the economy is the most important issue in the gubernatorial campaign here.

Whether Lehrman's expensive television advertising is paying off, or whether his unprecedented spending may alienate many voters, as Cuomo supporters hope, will only be known after the election next month.

Cuomo has tried to make Lehrman's campaign spending a major issue, but Lehrman insists he is not ''trying to buy the election.'' Rather, he insists, he is ''selling himself.''

Herbert Alexander, director of the Citizens' Research Foundation and professor of political science at the University of Southern California, said that Lehrman's spending ''skews the political process . . . it gives unfair advantage in terms of one candidate spending more money.''

Mr. Alexander said that ''Cuomo may have to obligate himself to certain interests'' such as labor unions to compete effectively against Lehrman's bankroll, much of which comes from his personal savings.

Armies of unpaid campaign workers helped bring about Cuomo's upset victory over New York City Mayor Edward I. Koch in the Democratic primary election in September. They are out in force now, manning telephones, scouring many minority voting districts for potential voters, and passing out campaign literature.

Recent polls range from ''too close to call'' to a New York Daily News Poll giving Cuomo a seven-point edge statewide and putting him ahead in heavily Democratic New York City 2 to 1.

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