A fouled-up armed robbery near New York City has refocused the familiar arguments in an old debate: Does the government need to spy on its own citizens to thwart a "Red menace"?

On one side are conservatives who were already pressing for a crackdown on "subversives" and now suggest that the fatal Brink's robbery exposed a resurgent leftist threat. The killings, they say, might have been prevented had it not been for restrictions imposed on domestic intelligence agents in the wake of Watergate.

On the other are civil libertarians who dismiss this as paranoid poppycock and say that nothing in our current system prevents the lawful pursuit of dangerous criminals.

The Oct. 20 ambush in the New York suburb of Nanuet left two police officers and a guard dead. But, tragic as it was, the robbery did not attract unusual attention until police identified the fingerprint of the once-notorious Weather Underground fugitive Kathy Boudin, who was captured along with two other members of the Weather Underground as they fled the bloody scene.

That revelation triggered a massive investigation by a joint federal and local task force, and FBI officials said early in the probe that they were looking at the possibility of links with other domestic leftist groups, as well as foreign terrorists.

The conservative weekly Human Events, The Wall Street Journal and a subcommittee on security and terrorism chaired by Sen. Jeremiah Denton (R-Ala.) are among the voices calling for a harder line on radicals and greater attention to their links with foreign interests.

And former FBI official Mark Felt said last week, "I will admit I have to bite my tongue" to keep from saying "I told you so." Felt and a colleague, Edward Miller, were convicted--and later pardoned by President Reagan--of authorizing illegal break-ins during the Nixon administration to pursue radicals having possible foreign ties.

But despite flights of rhetoric on all sides about the Nanuet robbery-murder, hard evidence so far points to a crime committed by people who wanted huge amounts of money and were willing to kill police officers to get it. Their motivation and ultimate intentions remain unclear as officials continue to mine the vein of leads unearthed by the botched robbery.

Informed speculation and indirect evidence made public to date suggest links between the Nanuet holdup and several earlier crimes--including a $300,000 Brink's robbery in the Bronx and the escape from prison of Black Liberation Army leader Joanne Chesimard, convicted of killing a police officer.

Evidence also suggests links between the suspects and a New York-based war of retribution against police, waged off and on for years by remnants of an old black power "off the pigs" faction. It is not clear whether the holdup gang represents "an amalgam of black and other groups, whether they've reorganized in a loose-knit fashion, or what," according to an FBI official.

It is unclear how important within the gang were the political goals of the Weather Underground members charged in the crime.

No evidence uncovered thus far connects foreign interests to the criminal network being flushed from cover in the wake of the Brink's robbery, according to the FBI.

Routine police work, tracing auto registrations, fingerprints and photos of suspects, among other things, led investigators to at least a dozen so-called safe houses from New York to Mississippi, where they found arsenals of weapons and ammunition, bomb manuals, diagrams of the Queens courthouse, police stations and duty rosters and leads to the whereabouts of other suspects in this and other crimes.

Police have arrested nine suspects (including two Weather Underground fugitives not implicated in the Nanuet robbery) and killed a 10th in a shootout. They are widening their dragnet for at least four others.

The known political underpinning of the crime so far includes the following:

The three Weather Underground members arrested after the Brink's robbery were wanted or had served time on bombing or assault charges in connection with political protests or terrorist activity, such as the 1969 "Days of Rage" in Chicago and the explosion of a Greenwich village townhouse in 1970, in which three leftist radicals died in their own bomb factory. Police and many former radicals alike say they had considered the group moribund for several years.

At least five others connected to the case are known or believed to be members of the Black Liberation Army or its parent organization, the Black Panther Party, or a black separatist group called the Republic of New Africa. These groups, too, were considered dormant, police said.

One of the female suspects in the Nanuet case, not previously known to be affiliated with these groups, had been charged in a recent violent protest against the South African rugby team and that nation's racial policies.

The groups, born out of the antiwar and civil rights upheavals of the late 1960s, preached violent disruption of society, couching their rhetoric in a potpourri of leftist revolutionary themes. (Boudin's strongest interest seemed to be feminism, according to acquaintances, and some of her writings expressed support for blacks as an oppressed people.)

Various leftist radicals have surfaced in recent years, sometimes accepting modest penalties for past offenses, and reentered Establishment society.

Eldridge Cleaver, former Black Panther leader, announced last spring that he had decided to join the Mormon Church. After a life in and out of prison, he said, "I want to be completely clean" with the law. He also said he favors the death penalty for violent crimes.

Most spokesmen still involved in the ragtag radical left or black power are keeping their distance from the Brink's shoot-out.

The Socialist Workers Party, once a subject of intense official scrutiny and currently party to a lawsuit against the FBI, issued a statement accusing the bureau of plotting to smear the group and "the entire workers' movement" by falsely charging that one of the suspects arrested in the heist, Judith Clark, is a "figure" in the party.

Former black power leader Stokely Carmichael was "on tour" and would not want to comment, according to an associate active in a militant black faction.

"This is a golden opportunity for the FBI to increase their budget at our expense and we don't want to participate in it," he said. He also "would never second-guess another black organization."

Still, for some, the potential threat from the left continues to loom like a gigantic shadow behind the reality.

The Wall Street Journal, in an editorial three days after the Nanuet robbery, accused American authorities of falling down on the job of investigating relationships between domestic radicals and "the intelligence arms of the Soviet Union and communist Cuba." The Journal described a new Canadian TV documentary that "depicts a deep involvement in American terrorism by Cuban intelligence, the DGI." The documentary is based heavily on an interview with Larry Grathwohl, a former Weather Underground member and sometime FBI informant, who says Cuban embassy personnel have served as communication conduits for the American underground.

"We suspect that a thorough investigation of the Nanuet case would show that we are dealing with much more than a group of spoiled brats turned vicious criminals," the Journal said. "We suspect the case would disclose that the Cubans have been actively aiding and abetting the Weather Underground and similar groups in the U.S. for years."

FBI official Roger Young called the Journal's charges of FBI inattention "utter nonsense."

The FBI has long been aware of contacts between traveling American radicals and foreign leftists, including the Soviet-backed Cubans, officials said. For instance, defense attorneys in the Felt-Miller trial introduced a 98-page summary culled from decade-old FBI files which ranged from a reference to Kathy Boudin's father, a prominent attorney identified as a member of the Comunist Party U.S.A. and a registered Cuban agent, to travels by Kathy to Moscow, where she spent her senior year of college, and to Cuba later. The summary also describes meetings in the Middle East among members of the Weather Underground, Eldridge Cleaver, representatives of North Vietnam and Palestinian guerrillas, among others.

Even so, while foreign interests may applaud and exploit radical activity in this country, authorities have been unable to produce hard evidence of foreign involvement in such activity.

The illegal "black bag jobs" that brought Felt and Miller to trial were "utterly fruitless," observes John W. Nields, the prosecutor in the case. "In fact the illegal searches were ruining the cases they did have; they had to drop a number of them" because of tainted evidence.

"There's no 'I told you so' on their side any more than on ours," he added. "No one at the trial disagreed that the Weathermen were violent and should be prosecuted."

To the consternation of the Denton terrorism subcommittee last spring, FBI officials asked for cutbacks in the bureau's domestic terrorism program, saying that such activity was not even near the top three on its list of priorities.

Although the "severity" of terrorist acts has been increasing, the number of such incidents has been declining in recent years, according to FBI officials. In any case, they add, agents respond to an individual incident such as Nanuet's in whatever force is required.

While FBI spokesmen have declined to comment directly on what limiting effects the controversial domestic-spying guidelines might have had, they said any investigations involving members of the Weather Underground or the Black Liberation Army have been focused in recent years only on individuals suspected of specific criminal acts.

Ten organizations, such as the Puerto Rican separatist group FALN, and 47 individuals were under investigation by the FBI in the last year under the heading of domestic terrorism, officials said.

Experts in terrorism note that even the most virulent European groups such as Germany's Baader-Meinhof Gang have failed to enlist large numbers, rarely exceeding three to five dozen members each.

The American culture, at its peak of social unrest a decade ago or in today's straight climate, apparently has not provided the encouragement to violence-prone radicals that some European countries have afforded.

Throughout the history of American protest movements, starting with the Wobblies at the turn of the century, "you find that the political system co-opted the grievances of the broader movement and in many cases co-opted the best of their leaders," says terrorism expert Brian Jenkins of Rand Corp. "This means that the political system robbed the terrorists of a constituency."