When Mayor Maynard Jackson began hiring permanent replacements last week for some 900 garbagemen and other low-paid city workers fired for going on strike, their union lost no time in drawing an obvious parallel:

"Remember that Dr. Martin Luther King Jr. went to Momphis in 1968 to march with striking sanitation workers who were members of AFSCME [American Federation of State County and Municipal Employees]," said a local union leader.

"He gave his life for them . . . Dr. King was fighting the same threats as are being made by Maynard Jackson."

The parallel is not lost on Jackson, the first black mayor of a major Deep South city. Despite a pro-labor record, and a series of official acts aimed at giving minorities and the poor more access to City Hall, he is the first black mayor to break a strike by mostly black, mostly low-income city workers who overwhelmingly supported his election.

Ironically, when the same AFSCME workers struck in 1970, Jackson, then vice mayor, sided with the workers and criticized former Mayor Sam Massell's firing of more than 1,000 of them. Those workers eventually got their jobs back after a 37-day strike.

A week ago, as the strains of "We Shall Overcome" floated through his City Hall window from voices raised in protest against his firing of the 900 workers April 1, Jackson turned to an aide and said:

"If anyone had told me four years ago that today I'd be on the wrong side of that song, I'd have called them a liar."

The dispute that put Jackson on the other side is bitter, even caustic, with roots deep in three years of steadily worsening relations between Jackson and AFSCME. It is also loaded with ironies, not the least of which is the mayor's belief that the workers had a just cause.

"Let there be no mistake about it," Jackson said two days after the firings. "The employees on strike need a pay increase. The employees deserve a pay increase. But we don't have it [the money]."

In an interview last week, he seemed to say that, however justified their cause, they should have taken his "no" as the final answer. Their list of demands, presented on March 10, 21 days before the March 31 cutoff date for raises laid down by the city charter, "was a package equating almost $10 million, which they knew was totally impossible. Why did they strike to get an impossible demand?" he said.

The city has never said what, if anything, might be possible, other than Jackson's offer Friday of a pay increase in 1978. The lack of any counter-offer infuriates the union. Both sides trade bitter charges of broken promises, bad faith, lies, deceit and trickery.

AFSCME does not buy Jackson's plea of poverty. The union points to the fact that Atlanta, unlike many major cities, operates in the black, that it has some $11.4 million in contingency funds set aside for future use, that property tax revenues for the past two years were under-estimated, that a $9.3 million cash surplus was carried over from 1976 into 1977.

City Councilman James Howard claims he called all the heads of city departments to go over their budgets, and found $17 million that was appropriated for specific items in 1976, but was not spent.

"Councilman Howard is whistling Dixie," the mayor responds. "The money is not there." The money Howard is talking about still has to be spent on the items it was originally appropriated for, he said.

Howard and the union argue that money for the pay raise is mostly a matter of priorities, that Jackson could, if he wanted to badly enough, cut back a bit on airport funding, water and sewer funding, and some other projects to shift money into a pay raise.

There are some close to Jackson who agree the mayor could try to do that. But they argue that the politics of the city, including strong anti-union feelings, the possibility of a 12-to-6 defeat by the city council on requests for money transfers, and howls of protest from Atlanta whites if airport or water funds are tampered with, make those choices even less acceptable politically.

The union has been asking for more money for a year now and voted to strike last July, but called that strike off after Jackson promised to do everything he could to find the funds.

The latest demand is 50 cents more an hour, or about $1,000 more a year.

Things are so sticky that the AFSCME accuses Jackson of using his reputation as a black liberal and a former labor lawyer to cover up the exploitation of city workers. Jackson accuses the AFSCME of making impossible demands on him because the union figured that, as a black mayor, he would be so protective of his reputation that he would give in rather than fight.

Although they won't admit it publicly, some national AFSCME officials are asking the same question Jackson asked: why did they strike? With only 1,290 employees organized out of 2,736 in AFSCME jurisdiction, and a solid support core of only 500 to 600, they knew even a well-planned strike would be difficult to win. And this one, they say, was not very well planned.

Their public answer is that the workers "may be a minority of the work force, but they're deep felt, bitter people," said one union official.

The strike did begin almost as a wildcat, with some 150 or so workers visiting City Hall, having a confrontation, with the mayor, and voting on the spot, and almost unanimously, to walk out the next day.

There is no indication that national AFSCME officials tried to discourage a walkout, even though Jackson had said during the strike threat in July that he would fire those who left their jobs. Georgia law prohibits governments from negotiating contracts with unions. Jackson has used the fact that he consults with unions as an example of how pro-union he is.

Atlanta is not considered a city friendly to labor. The Chamber of Commerce says only a very small proportion of Atlanta workers are organized, and those that are have given only perfunctory and lakewarm support to the strike.

Jackson's get-tough policy may have increased his popularity in the short run. A very unusual coalition has risen to support him. It ranges from Dr. Martin Luther King Sr., father of the slain civil rights leader, and the heads of the local NAACP and Urban League chapters, to a host of business leaders tied to the Chamber of Commerce.

Dr. King has said he knows the city doesn't have the money.

The chamber, which for 40 years virtually owned City Hall and dictated every major political and economic decision, has been cool toward Jackson during much of his term. Jackson was busy trying to reassert the independence of the mayor, trying to reach out for advice to other groups, and business leaders complained they weren't being consulted enough.

But the chamber likes his handling of the strike. Richard Kattell, president of the chamber and a leading Atlanta banker, said he thinks Jackson's actions have been watched approvingly by the medium-size, labor-intensive businesses like electronics assembling which the chamber is spending $300,000 a year to lure to Atlanta.

"It says to them, 'Look, here's a union that's trying to move in on City Hall and the mayor, even though he is black, and the business community, say no,'" Kattell said.

Even Bert Lance, the Atlanta banker whom President Carter picked to head the Office of Management and Budget, said that, while he hasn't been following the situation closely, Jackson looks stronger now. There had been talk that the downtown businessmen might run a candidate against him, but Kattell said he thinks Jackson is now a "shoo-in" for re-election this year.

The difficulty with such short term assessments, however, is that they may blow apart in the protracted fighting of a bitter, long-term war, which is exactly what Jackson's dispute with AFSCME has now become.

What had been the major issue, the 50-cent raise for employees averaging $7,400 a year, now appears secondary. What the union wants is to defeat Jackson at the polls in October -- even though it has no alternative candidate of its own. And to do that it is mounting a unique national advertising campaign.

The ads appeared for the first time in March 27 editions of The New York Times, Washington Star and Wall Street Journal. Right from the start, as intended, they drove the mayor and the Chamber of Commerce bananas.

"THE FALCONS AREN'T THE ONLY LOSING TEAM IN ATLANTA," read the bold headline. "TRY CITY HALL." The text accused Jackson of "four years of bickering, squabbling, phonyism and cronyism at City Hall," while the city ran downhill. It ended with: "The Falcons have hired a new coach. It's time for one at City Hall."

Nothing in the ads indicated that AFSCME was involved in a labor dispute with the city. The union says the ads were intended to prevent a strike, and the fact that they first appeared the day before the vote to strike was an unfortunate coincidence.

They had two purposes, the union said: getting under what the union perceived as the rather thin skin of Jackson to attack what it perceived as his huge ego; and getting the Chamber of Commerce to pressure the mayor into dealing more seriously with AFSCME demands.

In the short run, the ads have succeeded in making Jackson and the Chamber furious.

In the long run, the light could very well hurt the city, the mayor, the union, or any combination of the three.

In the short run, those likely to take the worst beating are the workers who no longer have jobs. There is the water meter installer, classified as Laborer 2 by the city, who has worked for Atlanta for 29 years, and earns, he says, $34.15 a day.

"A man who's been on the job that long, he should at least make $5 an hour," said one of his colleagues.

"If it wasn't for my wife working, I couldn't make it," said another man, a waterworks foreman with five children who said he made $42.82 a day.

"I voted for Maynard Jackson. I campaigned for him on my own time. But I wouldn't do it again."