President Carter's performance as peacemaker at the Camp David summit meeting has translated into a remarkable political triumph, winning new friends among the most hostile voters and respect for his abilities as a national leader.

A nationwide public-opinion survey, conducted by The Washington Post, found that Carter's popular standing went up dramatically - by 11 percent in just two weeks' time.

What is perhaps most significant: Carter made sharp gains among those citizens who have been most skeptical about his competence as president - moderates and conservatives and people who felt the man couldn't handle the job.

The Post's survey of 1,756 people, interviewed by telephone, offers an unusual glimpse of how one important event can quickly shift public attitudes. Post interviewers sampled opinion while the Camp David summit was under way. Then, after the dramatic climax, they called back a representative sampling of the same people, asking again how they felt about Carter as president.

Before the summit climax, the survey found President Carter in a virtual dead heat with former president Ford. Voters were asked for whom they would vote now if the 1976 election were being held again, and the results were 39 percent for Carter and 38 percent for Ford.

Last week, after the big headlines and dramatic TV exposure surrounding Carter's summit, the voters produced this result: 50 percent for Carter and 36 percent for Ford.

In this shift, Carter turned around two hostile regions of the nation - the West and the North Central states. Before Camp David, those regions preferred Ford. After Camp David, they supported Carter by substantial margins.

The political surge for the president was also reported by the Gallup Poll, which last week found Carter's "approval rating" at 56 percent - up 11 points since the first week of September and up 17 points since Carter's low ebb in early August. Citizens who disapprove dropped from 44 percent to 30 percent.

This is the first time in nine months that the Gallup Poll has found more than 50 percent of Americans who approve of Carter's performance. The new rating restores him to the approximate level of public popularity he held in the autumn of 1977.

What does it mean? No one can predict whether this surge will last. All presidents have experienced ups and downs in the polls, with upward surges following dramatic events that capture the public's attention.

In political terms, however, this new esteem gives Carter some breathing space he didn't have before. At least, it is a strong cautionary signal to the president's rivals, Republican and Democratic, who were sizing him up as an inept, one-tern president who would be easy to beat in 1980.

At the most, this warming of public opinion can give Carter an aura of authority, especially on issues of foreign affairs, which he has lacked until now. As the president takes on other controversial subjects, such as an arms-control threaty with the Soviet Union, it will be more difficult for his opponents to argue that he is an inexperienced amateur or that his leadership lacks public support.

"You've got to admit that he handled that aptly," a 32-year-old housewife in Houston told a Post reporter. "He had to be forceful to get them to come up with that agreement."

An auto mechanic in the same neighborhood said he is disappointed with many domestic policies of the Carter administration, but heartened by the Middle East agreement. "He's doing real good across the sea," the mechanic said.

In the southern Illinois town of Olney, the summit produced compliments for Carter, though many remain skeptical about the prospects for peace in the Middle East. "I think he's trying to do something good," said Eloise Ritchie, a grandmother.

"He should rate pretty high," said Alphonse Ishman, a retired farmer. "He took two guys there that were at each other's throats. Ain't they been fighting 20 years or like that? And he put them together. And for two or three weeks, all the word you heard was that they weren't getting any closer. So I don't think there's any question but he made a hell of a good shot at it."

The Post survey asked voters to rate President Carter's job performance on a scale from zero to 10. This is considered by many a more flexible and accurate gauge of public opinion in the long run, than the usual approach, which forces people to say yes or no, for the president or against him.

Carter's national average on this scale jumped 11 percent, from 5.4 during the summit to 6.0 after the summit. This is the equivalent of the gains that Gallup reports. The Post survey provides additional evidence of the political implications.

For example, 42 percent of those surveyed gave Carter a higher rating after Camp David. A few even jumped him on the scale from zero to 10.

Among those looking at Carter wit greater esteem were large numbers of people who have been most critical of him. After the summit, 48 percent of conservatives revised their rating of the president upward. So did 45 percent of those who call themselves moderates. Carter won higher ratings from 43 percent of the Democrats, 42 percent of the Republicans and 43 percent of the Independents.

The poll suggests clearly that many Americans have revised their judgments on Carter's competence - the question that contributed so much to his steady decline this year in public-opinion ratings.

In the original survey, the Post asked voters to choose between these two statements: "Jimmy Carter just can't seem to cut it as president," and "Jimmy Carter is a better president than he is getting credit for."

Almost 4 in 10 - 39 percent - chose the view that Carter isn't up to the presidency; 55 percent said he is better than his public reputation.

When the Post took its second survey of those same voters, it found that 45 percent of the critics and gave him a more favorable rating.

Another question suggests that, among a substantial minority of Americans, Carter has eclipsed Henry A. Kissinger as the foremost public figure identified with international problem-solving. The poll asked:

"For many years, Henry Kissinger tried to bring peace between Egypt and Israel. Just your impression: do you feel the new step toward peace between those countries show that Jimmy Carter is more able at peace negotiations than Kissinger was, or do you feel the new step toward peace was taken simply because the time was right for Egypt and Israel to come closer together?"

The answer: 21 percent think Carter is more able than Kissinger, 59 percent think it was a matter of timing and 6 percent think it was both. Thus, a quarter of the populace - 27 percent - now gives Carter the superior status as peacemaker.

One question polls cannot answer is: what will happen to Carter's popular surge if the Middle East peace frame-work falls apart? Voters' comments to Post reporters and the Gallup Poll suggest that many remain quite skeptical about the prospects for permanent peace, but they give the president high marks for a good effort.

"They're making it a show now, with all those men on TV every night," said Dora Garner, a housewife in Claremont, Ill., "but over the long run - I may be mistaken, I hope I am - I don't think it will turn out as big as they said the other night. They'll just keep on fighting."

The Gallup Poll found that 42 percent of those who heard about the summit still believe the new agreements will not lead to a lasting peace between Israel and Egypt. Only 31 percent are optimistic about that result.

Beyond his performance as summit negotiator, the Post survey found related evidence of popular regard for Carter's administration which contradicts conventional criticism in Washington. For instance, when citizens were asked whether Carter's so-called open style of administration was "healthy for the country" or whether it meant "you can't tell who's really in charge at the White House," people said it was healthy - by a 2-to-1 ratio.

One controversy surrounding Carter's White House splits the public right down the middle - whether he should fire any aides who use marijauna, regardless of how competent they are. A bare plurality feels that he should - 49 percent to 47 percent.

On a broader, more fundamental question, the majority perceives Carter as trying to reduce the size and the role of the federal government - which puts him in tune with a political theme that Republicans are trying to exploit for themselves this season.

A 78-year-old woman in Nashville expressed the warm personal regard which many voters hold toward Carter, regardless of their attitudes toward his official performance. "He's a good boy," she said, "many he's religious. You don't find that much anymore."

Even with his personal sympathy, many voters continue to see Carter as somehow inadequate for the high office - a substantial minority which could grow again if the president takes future stumbles.

"We all thought he'd sweep into Washington with a sword," said Rudy McNeely, a young Nashville song-writer, "but all he has shown is a pocketknife."

"Carter's a jerk," a Harriet Herman, a registered Democrat in Merrick, N.Y. "He's totally ineffectual as far as I'm concerned. He was very unprepared for the job, and is not getting the proper advice from the right type of people."

On a crass political level, people still are drawn to the excitement and celebrity of the president, regardless of disappointed or complaints with his record. For months, politicans have worried over whether to "keep their distance" from Jimmy Carter. But even before Carter's summit triumph, a substantial majority in the post survey agreed that a campaign visit this fall by President Carter would help, rather than hurt Democratic congressional candidates. After the summit, agreement rose to more than 4 to 1.