Bitter New York Mayor’s Race Shown as Tie in Polls : Election: Giuliani may have edge since some voters may not be telling truth. Dinkins needs help from fragile coalition.

This city’s bitter and close mayor’s race concludes today with questions about whether core supporters of David N. Dinkins will turn out as they did to elect him four years ago and whether some voters have been telling pollsters the truth.

The contest pitting Dinkins, New York’s first black mayor, against former federal prosecutor Rudolph W. Giuliani is an important test of the pulling power of President Clinton in a major urban setting. Clinton campaigned here twice for Dinkins, and a parade of Cabinet members plus First Lady Hillary Rodham Clinton has appeared urging voters to reelect him.

In the last election, Dinkins defeated Giuliani by less than 50,000 votes--one of the smallest margins in New York’s history--even though polls had shown him well ahead. This time, polls rate the rematch a statistical tie.

Giuliani’s advisers and some other politicians said Monday they believe some voters have been less than candid with pollsters and are reluctant to admit they will cast their ballots against Dinkins.

“He (Giuliani) was down 18 or 19 points last time, and we only lost by two,” a key strategist for the Republican and Liberal Party challenger observed confidently. “Now, we are neck and neck.”

The confidence was mirrored by the 49-year-old former U.S. attorney as he stood beneath a huge blue-and-white sign proclaiming “Rudy” and addressed cheering supporters at a Manhattan hotel.

“The people of the city are waiting for a new beginning,” Giuliani said. “ . . . The people who make up the old politics of this city have had their day and have done the damage.”

Dinkins is struggling to reassemble a fragile coalition of Jewish and Latino voters atop the solid base of African-American support that carried him to victory in 1989.

On Monday, he stood without an overcoat in raw weather near the front steps of City Hall to receive the endorsement of former Gov. Hugh Carey and Felix Rohatyn, the banker who played a crucial role with Carey in saving the city from bankruptcy in the 1970s.

Rohatyn said he backed the mayor “absolutely without hesitancy.”

“If you ever voted for me, vote for David Dinkins tomorrow,” Carey urged.

” . . . It’s not time for on-the-job training. There’s a team in the White House. We need a man to be part of that team,” the former governor said.

As the mayor accepted their accolades, a heckler wearing a raincoat and carrying a briefcase emerged from City Hall. “Go!” he shouted at Dinkins. “Go!”

Later, still scouring the city for votes, the 66-year-old mayor held a get-out-the-vote rally with black and Latino young people at a mid-town hotel. He was joined by Jesse Jackson and the Rev. Al Sharpton. Dinkins again attempted to frame the election in the simplest partisan terms.

A key question is whether Dinkins, who had a small army of 10,000 volunteers to get voters to polling places four years ago, can muster comparable enthusiasm in a city battered by the recession. Jealousy and rivalries over scarce jobs prevail among some of the mayor’s former backers. He has lost some union help. The United Federation of Teachers, which provided him with Election Day resources in 1989, is remaining neutral.

There is also a significant difference between Rudy I and Rudy II. Four years ago, Giuliani ran what many politicians agreed was an inept campaign. This time, Giuliani has had the guidance of political and media strategist David Garth, who successfully guided both John V. Lindsay and Edward I. Koch to the mayor’s office.

Giuliani has become personally warmer and far more disciplined in delivering the message that, in contrast to Dinkins, he would be a “hands-on mayor,” better able to tackle crime, the economy and substandard schools.

Giuliani has been endorsed by Koch. As the Republican and Liberal Party candidate, he is running as leader of a fusion ticket, with former Democratic Rep. Herman Badillo for controller and Democratic Councilwoman Susan Alter seeking the post of public advocate.