Washingtonians interviewed last night in an informal survey showed considerable sympathy for President Carter and his goals but also considerable doubt about whether his speech or his programs can meet the needs of the nation.

Several persons contacted immediately after the 10 p.m. address agreed in particular with the president's avowed aims of reunifying the nation and of freeing the United States from dependence on foreign oil.

"I thought he made a good speech," said Elonia Brown of D Street NE, a safe deposit custodian at a bank. "I don't think the president can lead alone," she added. "We need to get together."

One of the most optimistic of those contacted last night, Brown said she believed Americans can put into effect the energy programs sketched last night by the president, but she added: "They'll have to get together."

Bernice Friedlander, a congressional aide who lives in Northwest, was sympathetic to the president's goals, but skeptical about the chances of implementing the energy program.

"I don't know how much of what he said [he wanted to do] he can accomplish," she told a reporter. "This energy security corporation [mentioned by the president] sounds like a great idea. So does the solar bank."

However, Friedlander added, "I don't know that he has the clout to get it through [Congress.]"

"He's pointing in the right direction," said John Antkowiak, a retired Defense Department management employe who lives in Lanham. "I think we need to develop our own resources like he said."

Ken Pate, co-owner of a Shell service station in Lorton said, "If he [Carter] gets the program moving, it's going to hurt somewhat. But in the long run, economic independence is worth it."

Contacted by telephone at his home in Hyattsville, Anthony Manzanares, a retired printer, also expressed satisfaction with the president's goal of independence from foreign oil producers. "We are the greatest nation in the world and we have the most resources in the world," he said. "I don't think we need to go to anyone."

Of those reached by The Post for brief interviews after the nationally televised speech, several persons were quick to characterize the President and his performance as honest and sincere.

Alice O'Connor, a student at Trinity College in Hartford, Conn., who is living in Georgetown this ummer, called the address "very honest," even while assessing it as "not quite inspiring enough."

She said that Carter, in likening his energy programs to a military campaign, was "appealing to a patriotism that I'm not sure is there."

Even in a quick, informal survey, skeptics and doubters were easy to find.

"He just hasn't said anything substantive," wailed a 29-year-old social worker who was among about 25 persons watching the speech at the Hawk and Dove Restaurant on Capitol Hill.

"He's like a coach giving a pep talk before a football game," asserted the woman, who declined to giver her name. "But it doesn't inspire me."

"I think the president's a man lost in a large cave and the light is out and he wants us to rescue him," said Casby Johnson, a retired fireman, of Anacostia Avenue NE, who was interviewed at home. "If we had the resources that he says we do," Johnson said, "why don't we use them."

The speech, Johnson said, "may help unify the nation, but I don't know . . . People are going to do what they want to do anyway."

"I'm disappointed," said retired Army Col. Thomas T. Zerick of Springfield. "But then again, I didn't expect much . . . He has not set any examples, he has not led us like a president should."

Ray Smith of Crystal City, a federal employe, also was disappointed by the speech. He called the long-awaited address "22 minutes of what everybody knows and . . . about eight minutes of pretty things that should be done" without details of how to do them. "I don't think we learned anything," he said.