The President of the United States is coming to town.

Jimmy Carter, whose campaign supporters claimed he would make this city his adopted home, has finally gotten around to scheduling a major appearance before a hometown crowd.

On Oct. 13, Carter will speak at the Kennedys-King Day fundraiser sponsored by the D.C. Democratic State Committee. Admission is $125 a plate.

His election brought great expectations of a new-style presidency as the born-again Baptsit from the deep South took up residency in this city, where small-town traditions are strong, gospel music extravaganzas draw thousands and the overwhelmingly black city electorate gave Carter 82 percent of its votes.

A key presidential adviser on city affairs told a reporter shortly after Carter's inauguration that Carter would be at home in sections of black Washington where other chief executives would not. Among the ideas the aides were considering to boost the president's local presence was a weekend trip to Anacostia Neighborhood Museum or even a breafkast of grits at the Florida Avenue Grill. Neither has taken place.

And Carter appears to have passed up other opportunities to get involved in the city that surrounds the White House.

Last fall, for example, when he wanted to answer grassroots questions about his civil service reform plan, Carter chose a high school in Fairfax for the town hall meeting.

Earlier this year, the D.C. Federation of Civic Associations asked the president to have a town hall meeting with them. The White House declined.

The Advisory Neighborhood Commission for the area of the city that includes the White House, the Foggy Bottom-West End ANC, invited their new neighbor to some of their meetings. He did not come.

Carter's daughter Amy does attend a city public school, the Hardy Middle School, off MacArthur Boulevard. NW (she had previously attended Stevens Elementary downtown), and members of the first family have attended some school functions. And, in the only notable hometown appearance since being president, Carter took part in the 113th anniversary celebration of Zion Baptist Church in Northwest Washington two years ago.

Beyond that, Jimmy Carter's Washington has been the Washington of the Federal City -- art exhibits at the Corcoran Gallery and concerts at the Kennedy Center. His church, First Baptist, at 16th and O streets NW, is right up the street from the White House.

First Lady Rosalynn Carter took a tour of riot-scarred H Street NE, did fix-up work at D.C. General Hospital and helped dedicate the Capitol Children's Museum. She also gave a White House luncheon for members of the Federal City Club. But that was months ago.

Nowadays, the best predictable view of the first family on the local scene is on 17th Street NW, not too far from Dupont Circle. Chip Carter, the president's son, is a lunchtime regular at the Fox & Hound Lounge there.

Everett Scott, president of the Federation of Civic Associations, said recently, "As president, he has shown very little interest in affairs of the District. The city as a whole seems to have been put on a back burner since Carter came in."

Scott said, moreover, that he thinks the anti-Washington rhetoric that Carter takes with him around the country hurts the national image of the District of Columbia, which is already seen, Scott said, as simply a town where congressmen and top level bureaucrats live, with no genuinely local population of its own.

That attitude is one of the impediments that some supporters of the city's drive for full voting representation in Congress consider significant. "He has a bad attitude as it relates to Washington, D.C., period," Scott said. "What he's doing is kicking the people of the District of Columbia in the butt, to be very honest."

Such hostile feelings generated in part by presidential no-shows in hometown Washington may help to explain why nearly half the members of the D.C. Democratic State Committee, Jimmy Carter's official host for the Oct. 13 affair, are predisposed to dumping him next year.

Twenty-eight of the 64 members of the state committee also belong to the D.C. Committee for a Democratic Alternative, which is publicly an ABC (Anybody-But-Carter) organization, and actually a group favoring the still undeclared candidacy of Sen. Edward M. Kennedy for the Democratic nomination in 1980.

"I remember when he said he intended to be a resident of Washington, D.C.," recalled Barry Campbell, cochairman of the Alternative Committee. "Aside from the symbolic expression of enrolling his daughter in D.C. public schools, I really haven't seen that become a reality."

Sharon Pratt Dixon, the Democratic National Committeewoman who says she is still neutral on the race, would not link Kennedy's assumed popularity with Carter's lack of presence here. But, she said, "I guess we suffer the brunt of being the federal city.The president is here so often. When he schedules time, he schedules time where his presence is less felt (on a day-to-day basis). The District of Columbia gets lost."

"His presence Oct. 13 will be a big help for him," Dixon said, "because obviously we don't want to be taken for granted."

In some respects, it's too bad for Jimmy Carter. He really has been good to the District when it comes to supporting increased budget autonomy, a higher federal payment, greater local authority to prosecute criminal offenses and choose local judges and, to some degree, full voting representation in Congress.

But there is still no real Jimmy Carter presence in this town, and any effort now risks being seen as merely a preelection year attempt to recover his losses.

That could hurt Carter if Kennedy does enter the race and, as some observers speculate, uses the May 6 District of Columbia Democratic primary to show that he can beat Carter among blacks, who voted overwhelmingly for Carter in 1976.

Kennedy will not be at the dinner Oct. 13. His sister-in-law, Ethel, may come as a stand-in, dinner planners say. Former United Nations Ambassador Andrew Young will be there, and that should help Carter, since Young is strongly supporting the man whose administration he recently left.

But even with Young, says "Dump Carter" leader Barry Campbell, the president's appearance may simply be too little too late.

"At this point, we've had three years to review his record," Campbell said."I doubt that in one speech he'll be able to change many minds."