N.Y. Mayor’s Race Draws National Partisan Interest : Politics: Election of a Republican mayor in the nation’s largest city could cause problems for a possible presidential bid by Gov. Mario M. Cuomo.

The increasingly close mayoral race in New York City has become a high-stakes political battleground, as the White House and the Democratic National Committee are trying to affect the outcome.

When Republican Rudolph W. Giuliani’s mayoral campaign was on the verge of running out of money recently, President Bush came to the rescue, raising $1.5 million at a dinner in Manhattan that allowed the candidate’s commercials to remain on the air.

First Lady Barbara Bush will host a luncheon for Giuliani next week, and three Cabinet secretaries plus White House Chief of Staff John H. Sununu will be in New York to give the Republican contender more support.

On the other side, Sen. Edward M. Kennedy and Gov. Michael S. Dukakis of Massachusetts are campaigning for David N. Dinkins, the Democratic mayoral candidate. Democratic Sen. Bill Bradley of New Jersey is expected to campaign for Dinkins soon, and New York Gov. Mario M. Cuomo and Democratic Sen. Daniel Patrick Moynihan campaigned at Dinkins’ side Thursday.

Part of the reason for the intense national interest plays into nascent presidential politics. The election of a Republican mayor in the nation’s largest city could send a cannon shot across the bow of any presidential ambitions Cuomo may harbor.

An activist mayor of another party would be in a strong position to be a political thorn in the governor’s side, distracting Cuomo from national issues and limiting out-of-state travel.

Previous mayoral-gubenatorial squabbles have damaged presidential hopes. Mayor John V. Lindsay bitterly fought with former Gov. Nelson A. Rockefeller, and Lindsay’s criticism of Rockefeller for failing to call out the National Guard during a bitter garbage strike in New York City reverberated nationally. When Rockefeller ran for President, conservative Republicans attacked the reluctance of the governor to summon the Guard.

Registered Democrats outnumber registered Republicans in New York City by five to one. And in an effort to mobilize his natural Democratic base, Dinkins has sought to picture Giuliani as a creature of “Reagan Republicanism,” uncaring about the plight of the inner cities.

On Thursday, Cuomo once again underlined that theme when he appeared with Mayor Edward I. Koch and Moynihan at a rally for Dinkins in Manhattan.

“The national Republicans, who have announced they want to establish a new beachhead . . . in New York by winning this election, have declared war on our cities for the past eight years,” Cuomo charged.

In a new Dinkins commercial, Kennedy attacked Giuliani for calling for a reversal of the Roe vs. Wade U.S. Supreme Court decision legalizing abortion. Giuliani changed his position on abortion during the campaign. He now supports the right of a woman to have an abortion, plus public financing of abortions for the poor.

When President Bush first praised Giuliani at a Republican dinner early in the campaign, he mispronounced the candidate’s name. But at a dinner for Giuliani this month, he was a potent fund-raiser.

And as polls showed the race growing tighter, Sununu and three Cabinet secretaries, Jack Kemp of Housing and Urban Development, Samuel K. Skinner of Transportation and Nicholas F. Brady of Treasury, have scheduled fund-raising events for Giuliani in New York.

A spate of polls was made public Thursday. A survey for New York Newsday conducted by the Gallup Organization gave Dinkins a 12-point lead, but a WNBC-TV/New York Post poll put the Democrat’s lead at only 5 points, in line with a recent Daily News-WABC-TV poll showing a 4-point lead.