This city's mayor, William Green, is all but certain to endorse Sen. Edward Kennedy for president this week, a potentially far-reaching event that points up defects in President Carter's unique reelection campaign.

That Bill Green should wait so long to endorse old pal and family friend Teddy Kennedy is partiallly attributable to the darker side of the Carter method: the implied threat of retribution against cities whose mayors oppose the president. But that same method's studied snubs of this city's new mayor have forced him to end up as an enemy.

A Green endorsement could be the added edge enabling Kennedy to win the Pennsylvania Democratic primary April 22. Green's backing of Kennedy firms up an apparently substantial lead in Philadelphia (about 20 percent of the state Democratic vote) and also builds Kennedy's prestige elsewhere in the state.

The prospect that the Kennedy challenge will be prolonged nationally by Philadelphia can be traced to the Carter method. It is light on lofty poetry and heavy on pedestrian elbow grease: meticulous attention to pretty details such as ballot placement of delegates, social amenities and minor government largesse from Washington, surprise presidential telephone calls to political hacks. Its darker side is shrouded in vindictiveness and coercion.

That darker side is seen in Carter's attitude toward Philadelphia, a city 119 miles from Washington he has never visited as president. The overt reason for his absence was the embarrassing presence until January of Frank Rizzo as a maverick, right-wing Democratic mayor. But Democratic politicians here believe Carter neither forgave nor forgot that Philadelphia voted against him in his climactic 1976 Pennsylvania primary triumph.

Replacement of Rizzo by the incomparably more congenial Green did not help. Green's personal ties with Kennedy led the White House inner circle to dismiss his professions of neutrality. That ignored this truth: Green, sobered by harsh realities of municipal finance, is appalled by Kennedy's open-handed economic liberalism.

Consequently, a little presidential romancing might have secured Green's neutrality. Instead, there was a cold shoulder, and not because of presidential preoccupation with Iran. "Invitations for tea at the White House came to everybody and his brother, but not to Bill," a Green insider told us. Carter has been busy telephoning low-level politicians such as city Registrar of Wills Ron Donatucci, Democratic leader of the 26th ward in South Philadelphia where the president needs help. No calls went to the mayor.

What Green has received from Washington is a little carrot and a little stick. The carrot: Secretary of Commerce Philip Klutznick came here to reveal that Philadelphia had won out over Lynn, Mass., for a $2.2 million shoe research facility (Pennsylvania no longer manufactures shoes, but Massachusetts voted for Kennedy). The stick: although legal impediments had been cleared, urban development grants for Philadelphia remained stalled in Washington.

That stall suggested a broader threat that this city would suffer cruelly if its mayor opposed the president. "I would rather that Bill kept neutral," one local Kennedy leader confided. "We need the federal money more than Kennedy needs Green."

The mayor has been playing it both ways. While he maintains public neutrality, his fund-raisers have raised money for Kennedy. David Glancy, Green's new hand-picked city chairman, has been officially neutral but privately pro-Kennedy.

Apart from future blockages in the federal money pipeline, the president's present budget cutbacks prompted quick retaliation. District Attorney Edward Rendell, a dynamic new political presence here, reacted quickly to Carter's cut of law-enforcement grants by breaking his self-imposed restriction on political endorsements and coming out for Kennedy. Simultaneously, there were signs of black voters' turning away from Carter.

So, Green and his inner circle asked themselves just how real the president's power to hurt or help Philadelphia is. What had Mayor Richard Caliguiri's early endorsement of the president won for Pittsburgh? "A lot of invitations to the White House," replies a close associate of Caliguiri.

At this writing, Green appeared ready to join the Kennedy trend in a city where unemployment always has eclipsed moralizing as a political issue and, says a friend, to "make himself feel better by getting right with Teddy." aThat ultimately may not detour Carter's majestic path to a second term. But if it does, it will call into question the politics of pork, threats and retribution as practiced by the president's men.