ST. GEORGE'S, Grenada

Even though Washington wants a swift end to its military presence here, the job of getting the remaining U.S. troops off the battle-scarred island could take longer than anyone expected.

Three weeks after the October 25 invasion by the U.S. and six Caribbean states, an interim government barely has begun functioning. A multinational force to replace the 3,000 Americans still here has yet to take shape.

Also working against the Reagan administration's self-imposed withdrawal deadline of December 1: The fact that many Grenadians have come to view the U.S. troops as liberating heroes and want them to remain at least through still unscheduled elections.

Without the Americans, the prevailing feeling is that essential public services may never be restored, the island will go unprotected and Havana and Moscow will try to recover their influence by restoring a Marxist regime. "You shouldn't leave too soon," comments a worried shopkeeper. "We need protection."

If President Reagan decides to provide such protection, he found himself in mid-November free to keep troops here for as long as the Grenadians think may be necessary. Congressional opposition was fading. A delegation of once skeptical House Democrats returned from an inspection trip convinced that the action was justified. Even House Speaker Thomas O'Neill, who has been one of the President's most persistent critics, suddenly changed his mind.

"The overwhelming consensus of members of the delegation was that a real potential threat to American citizens existed in Grenada," said the Speaker. "Since this was the case, I believe that sending American forces into combat was justified under these particular circumstances."

Following the mission, Congress displayed markedly less interest in imposing the War Powers Act, which would require Reagan to seek lawmakers' permission for keeping troops on the island for more than 60 days.

For their part, U.S. military leaders told Congress they still hoped to be out of Grenada by early December. But one of them, Army Gen. John Wickham, cautioned against leaving behind "a nascent insurgency" that could undo the achievements of the invasion.

Grenada's British-appointed Governor-General Sir Paul Scoon took the first step toward reviving the political process here by announcing on November 9 the appointment of a transitional regime to be headed by United Nations Deputy Alistair McIntyre. None of the nine appointees to the council, said Scoon, has either political ties or a vested economic interest in Grenada.

The immediate task of the temporary government is to restore government services and begin mending the economy, both of which are daunting tasks that require a large degree of national cooperation.

In a bid to pick up the support of remnants of the leftist New Jewel Movement, the council plans to retain at least some programs initiated by the late Prime Minister Maurice Bishop, who was ousted and killed by his Marxist partners. His New jewel regime earned high marks for social reforms.

The government also is encouraging organization of local political groups to take part in the elections. Among them are backers of Sir Eric Gairy, the former Prime Minister whose erratic rule was over thrown by Bishop in 1979. Hopes remain high that free elections will usher in a period of stability. But it is becoming increasingly evident to many here that this may not be possible without at least a token U.S. military presence.

Prominent church leaders warned visiting U.S. congressmen that a premature withdrawal would invite disaster. One cause for alarm is the prospect of 400 young Grenadians returning from studies in Cuba radicalized and bent on revolution. "We are afraid of falling back," says a churchman. That concern is echoed in pro-American messages that have been read in every pulpit on an island where 1 out of 2 residents is a practicing Roman Catholic.

Emotionally, Grenada is far from being back to normal. The country still is reeling from the chaotic events of the past month that saw Bishop murdered in a bloody coup and a 15,000-man U.S.-led task force suddenly invade.

Reminders of the turmoil are everywhere. Searches continue for mass graves, and corpses still are being discovered, including one thought to be that of Bishop. There is the tooth-rattling racket of munitions being detonated by U.S. bomb-disposal units. That noise mingles with sporadic sniper fire from a handful of Cubans who took to the hills after the fighting.

The threat of terrorist acts against American soldiers is being taken seriously-a fear that is shared by many Grenadians who helped the invaders. People expect reprisals from hard-core hew Jewel revolutionaries who remain free. "You are letting the bad people go," complains a jobless carpenter in St. George's. "You should lock them up. They aren't finished."

As U.S. officials try to restore order, the American presence has become both more permanent and more obvious. The huge container ship American Eagle virtually filled the tiny harbor before disgorging some 828 pieces of construction equipment, as well as crate upon crate of American soft drinks and food. Another big U.S. container ship was at anchor offshore, awaiting its turn to unload.

Construction of what could be used as a U.S. military station is under way at Point Salines, site of a controversial 10,000-foot-long airstrip built by the Cubans. Other Army men are repairing the water system, fixing pipes and pumps. Roads cratered by explosions are being paved.

A 33-man Army civic-action squad has been assigned to help smooth out community relations. A "psychologicaloperations team" is running the radio station. Its members also are assigned to plaster the island with posters saying good things about the invasion.

Washington originally hoped that a military force made up of troops from British Commonwealth nations would be sent here to insure security. But the momentum has slowed as controversy over the invasion and U.S. occupation has ebbed.

Now, Grenadians say they are considering a Commonwealth security force only as a "contingency plan" against the day that Americans leave.

With each passing day, it becomes more clear that the U.S. Presence here will be seen for months, not just weeks.