POLITICS : N.Y. Governor’s Contest Shaping Up as Liberalism’s Last Stand : Seeking his 4th term, Mario Cuomo is running the race of his life. His ideology and record are key campaign issues.

Gov. Mario M. Cuomo, one of the last surviving icons of American liberalism and a man many Democrats had thought surely would one day lead their party from the White House, today is battling to save his political career from extinction.

At 62, Cuomo is regarded outside New York as the last governing liberal, the leading torch-bearer for what remains of that once politically potent faith in the problem-solving abilities of activist government.

But at home, as he seeks a fourth term in Albany, he is in danger of being driven from public life by a little-known Republican state senator named George Pataki, whose principle strength appears to be that he is not Mario Matthew Cuomo.

A direct heir to the New Deal philosophy that an earlier New York governor, Franklin D. Roosevelt, used to define the modern Democratic Party, Cuomo reflects in his own background and beliefs the diverse alliance of social and ethnic groups that dominated big-state politics for more than a generation.

But these doctrines and forces are in decline in New York as almost everywhere else. Not only have many voters grown cynical about the problem-solving ability of government, many now care more about making the society around them safer than about making it gentler. And the old alliance of labor unions, immigrants, ethnic groups and liberal intellectuals has lost political cohesion and crusading energy.

The result for Cuomo has been a sharp slide in popular support. A new poll released last week by the widely respected Marist Institute of Public Opinion showed Cuomo trailing Pataki by 44% to 38% among registered voters. That amounts to nearly a statistical dead heat because the poll has a sampling error of plus or minus 3.5 percentage points, but it still represents a stunning loss of support for Cuomo.

Just as troubling from the governor’s point of view, the survey of 900 registered voters showed that Cuomo’s approval rating in the state he has governed since 1982 is barely above 30% and that three of five New Yorkers believe their state is headed in the wrong direction.

So the contest here shapes up as liberalism’s last stand. And Cuomo’s Republican foes view him as a sort of latter-day Gen. George Armstrong Custer, who is about to lose his political scalp.

“We are going to win the race on Nov. 8 and there is going to be no fourth term for Mario Cuomo,” Pataki told a boisterous crowd of about 300 GOP loyalists in Hicksville in Nassau County recently.

“All the Democrats where I work are going to vote for Pataki,” claimed one of the guests, Beatrice Larucca, from nearby Levittown, who is collections manager for a bank. “They want the death penalty,” she said, referring to Cuomo’s longstanding opposition to capital punishment, which Pataki advocates. “And they are just tired of Cuomo.”

Exacerbating Cuomo’s problem is continued anxiety about the state’s economy. Despite the gains made in the last 18 months as the nation has pulled out of recession, about 60% of those surveyed by the Marist Institute said they believe their state is still in a slump.

“Things have gotten better only slowly. And people aren’t sure they are going to stay that way,” Cuomo campaign chairman John Marino said in an interview. “That’s true not only in New York but all around the country.”

Yet Cuomo clearly has not tired of being governor. In the face of adversity he displays the same energy and will that has made him a power in the nation’s second-largest state for more than a decade and the beau ideal of liberal Democrats around the country.

“This is one of the most innovative and most exciting schools in the city,” Cuomo told a reporter recently as he bounded up the steps of Intermediate School 218 in Inwood. “Keep your eyes open,” he urged. “These kids and teachers have great ideas.”

Inwood is one of many New York neighborhoods that have been ravaged by poverty and neglect. The governor was there to accept a $10-million federal grant to help schools better prepare their students to take jobs and start businesses.

And to give Cuomo an extra boost, the Clinton Administration had dispatched Labor Secretary Robert B. Reich to deliver the grant personally.

“The governor has set a national standard for an active government, applying new ideas to improve everybody’s life,” Reich declared.

Cuomo’s campaign challenge is twofold. On one hand he must convince New York’s middle-class moderate voters that he does not fit the image of irresponsible spender and taxer that the Republicans have carved out for him. On the other, he must stir enough enthusiasm among the New York Democratic Party’s remaining liberal cadres--minorities, union members, feminists and the like--to get them to the polls.

To refute the big-spending charge, Cuomo has promised to disclose plans before Election Day to cut more than $1 billion in taxes. He has also pledged to strengthen the tax base by increasing efforts to foster the growth of high-tech industry in the state. At the same time he has been striving to revive longtime allegiances among New York’s myriad minority groups by sounding the traditional battle cries of the liberal past.

Talking to the intermediate school students, he reminded them of his own difficult origins as the son of immigrant Italian parents. When he recently discovered from an old report card that he had been absent for 38 days in his first term in school, Cuomo said he asked his aged mother if he had been sick.

“What do you mean sick?” his mother retorted, according to Cuomo. “I breast-fed you until you were 3 years old to keep you healthy. You were absent because you were ashamed to go to school because you couldn’t speak English.”

Rising from those humble roots, Cuomo earned a law degree at St. John’s University, won recognition as a private attorney and battled his way through the echelons of New York state politics before laying claim to the governor’s office in 1982.

In 1984 he became a national figure with his impassioned keynote speech to the Democratic National Convention that nominated Walter F. Mondale for President. He urged Americans to “look past the glitter, beyond the showmanship” of Ronald Reagan’s presidency to see that “there are people who sleep in the city’s streets, in the gutter, where the glitter doesn’t show.”

Though the speech stamped him as one of liberalism’s most eloquent spokesmen, in his home state some Democratic critics complained that his deeds failed to fulfill the promise of his liberal rhetoric, noting that he took advantage of the booming economy of the ‘80s to cut personal income tax rates rather than to launch new social programs.

But Cuomo did much to back the government programs that liberals admire, increasing spending on education, expanding health insurance coverage and plowing $50 billion into roads, bridges and mass transit systems.

The crunch for Cuomo came with the onset of the 1990 recession, which forced him to cancel the third installment of a three-year cut in personal income taxes and to raise several other levies. It is these increases that have provided ammunition for Pataki’s efforts to depict Cuomo as a big-spending liberal.

Cuomo prefers to describe himself as a “progressive pragmatist.” But when he was asked, after his talk at the intermediate school, about the slogan aired in Pataki’s campaign commercials--”Mario Cuomo: too liberal, for too long”--Cuomo sought to give his own meaning for the dreaded “L word.”

“If liberal means that I want to see these children be given at least the opportunity I had, then I am a liberal,” he said. “If liberal means I want everybody to have health care, then I’m a liberal. If liberal means building more prison cells than all other governors in the history of New York state built, then I’m a liberal, because I did that.”

Even as their candidate strives to define himself, Cuomo’s strategists are hoping to label their opponent, Pataki, as out of step with the moderate tradition established by four-term GOP Gov. Nelson A. Rockefeller, who in 1970 was the last Republican to win that office.

But the 49-year-old Pataki, whose genial manner belies his ambition, does not offer much of a target. In his 10 years as a legislator, he authored no major legislation. And in a welfare reform package offered last week, Pataki steered away from drastic measures proposed in other states to cut welfare beneficiaries from the rolls. Instead he concentrated on milder proposals to increase the number of welfare recipients taking public service employment.

But most analysts agree that the main issue in this campaign is and will remain Cuomo and his record. And Pataki is expected to avoid making proposals that would make voters forget their disenchantment with the incumbent governor.

Along with the ideological baggage he carries, Cuomo also suffers from the New York version of anti-incumbent fever. And in Cuomo’s case this resentment is probably reinforced by reaction to his forceful personality; admirable at times, it can also be abrasive, even to his admirers.

In this sense Cuomo may be the quintessential New Yorker whom even New Yorkers after 12 years find hard to take.

Speaking to a group of supporters in Manhattan last week, Cuomo conceded as much, saying: “There are a whole bunch of people who say, ‘Mario, for God sakes, 16 years. Are you kidding? What the hell is this? Did you inherit the office?’ ”

But Cuomo shrugs off his difficulties, saying: “It will be close for a while but not as close as you think. I’m going to be around for four more years.”