A battered politician named Jimmy Carter, surrounded by mutinous noises from his own party, is reminding the faithful that Jimmy Carter has been down before and always springs back on top.

At the White House on Friday, another collection of several hundred Carter delegates to the Democratic National Convention was convened for the president's personal pep talk. He reminded them that they, too, have been scorned in the past, saying:

"This time eight months ago, if most of you had said, I'm going to run as a Carter delegate," the chances are folks would have said, 'Aw, you'll never win.' But, YOU ALL WON! Right? And you're going to New York."

The Cartr delegates responded with lusty cheers, and their buoyant demonstration of loyalty to the presidnet provides a useful and realistic check on the current storms and intrigues of political Washington.

Carter is in trouble. Many party leaders, privately or publicly, would like to see him replaced at the head of the Democratic ticket this fall. But the outcome of next month's convention in New York City is going to be determined by the elected delegates, not by members of Congress or party elders.

And Carter has the delegates. He won 24 of the 34 primaries. He received 51 percent of the total votes cast in the Democratic contests. Of 3,311 delegates going to New York, 1,971 are pledged to Carter -- 305 more than he needs for majority control and the nomination.

This baseline reality is easy to forget in these bizarre days between the Republican and Democratic conventions. Rumors of defection and mutiny and an "open" convention are all over Washington. Republicans are talking about "Billygate" with an earnestness that barely conceals their delight. Sen. Edward M. Kennedy (D-Mass.), who lost in those 24 Democratic primaries, still talks about winning the nomination. And an assortment of Capitol Hill Democrats and nonelected party leaders are yearning to find an "alternative" candidate.

There is little doubt that the Billy Carter affair and the president's sagging popularity in opinion polls have shaken the Democratic establishment in Washington.

"No one would contradict that there is a queasiness among Democrats here, a feeling that this might be the 'Eagleton' of the Carter campaign," said Rep. Andrew Jacobs Jr. (D-Ind.).

That queasy feeling is reflected in the newly launched effort by about three dozen House Democrats to move the convention delegates away from both Kennedy and Carter and to find some less-objectionable nominee.

The House members are reflecting the strong instinct for self-peservation endemic among elected officials. "As you get closer to an election, anything with an unfavorable twist gives concern to any candidate," Rep. Melvin Price, a senior Democrat from Illinois, noted the other day.

But the various "dump-Carter" movements are bucking some fundamental political realities.

For one thing, the numbers are all with Carter -- he has 700 more delegates than his only competitor, Kennedy.

And the Carter delegates are, beyond question, dedicated Carter delegates. Many of them -- like those who gathered in the White House Friday -- signed up for the president last fall when Carter was considered a sure loser to Kennedy. Most of them were tested for loyalty by the Carter campaign leaders, and proved themselves true-blue. Thus, there are not many Carter delegates identified as wavering. That kind was weeded out in the caucuses and party meetings where delegates were chosen.

The formidable task facing anyone who wants to dump Carter at the convention was reflected in an Associated Press poll of 2,200 Democratic convention delegates around the country. It found a total of only four Carter delegates who are willing to tell a reporter that they might switch to someone else.

The Kennedy campaign, which has its own delegate canvassing operation, has found the same situation. Kennedy's people cannot claim any more than a handful of delegates who might move from Carter to Kennedy at the convention.

The Kennedy camp's official explanation is that there may be many more potential switches out there somewhere, but these delegates are keeping quiet for fear of retribution from the Carter camp.

Another possible explanation is that there are just not many Carter delegates who have even thought about deserting the president.

If any significant number of Carter delegates develop second thoughts about their candidate, there is still another major obstacle confronting dump-Carter enthusiasts -- finding someone else to replace him.

Kennedy has been roundly rejected by the Democratic voters already this year. The White House yesterday characterized the House members' efforts to find a replacement as "very clearly a Kennedy-inspired operation that attempts to take advantage of the president's difficulty right now."

But tose who attended the House members' meetings said it was clear from the discussions that Kennedy is not a viable alternative to Carter.

If not Kennedy or Carter, then who?

Secretary of State Edmund S. Muskie, age 66, was once defeated for the nomination. Sen. Henry M. Jackson, 68, is only one year younger than Republican nominee Ronald Reagan, and was twice defeated for the nomination. rVice President Mondale was Carter's right-hand man in the primary campaign, and spent the last six months extolling Carter's virtues as a leader.

All of those possibilities and others would please some elements of the Democratic coalition, but they would also enrage others. Too liberal or too conservative, too young or too old. In short, it's hard to come up with the name of a Democrat who is well known and could also unify the party.

Meanwhile, with the usual thoroughness the Carter people bring to electoral politics, the president's campaign has diligently tended to its own delegates, keeping them happy, well-informed and loyal. Twenty-two people on the Carter-Mondale reelection committee are working full-time keeping tabs on delegates. Every Carter delegate has been invited to the White House at least once, some two or three times.

When 200 to 300 of them were here Friday, six Cabinet-level officers met them for lunch at the Mayflower Hotel. Democratic National Chairman John White gave them a pep talk on the party. Campaign National Chairman John White gave them a pep talak on the party. Campaign manager Tim Kraft gave a pep talk on the campaign. National Security adviser Zbigniew Brzezinski talked about international issues. White House domestic adviser Stuart E. Eizenstat talked about domestic issues. Secretary of Health and Human Services Patricia Roberts Harris talked about Carter's accomplishments. And White House adviser Anne Wexler led the delegates point-by-point, day-by-day, through what they can expect at the convention.

Afterward, they all trooped over to the White House for a reception in the East Room with the president and Mrs. Carter.

About 250 Carter delegates, attended a similar affair on July 19; 600 are invited to Washington next Friday.

Kennedy, meanwhile, is doing the same sort of thing with his delegates, on a much more modest scale. Yesterday the last son of the party's best-known family hosted the chairmen of each state's Kennedy delegation, plus about 250 New England Kennedy delegates, at his Squaw Island home in the Kennedy compound at Hyannisport. The delegates were briefed by Kennedy political strategists Carl Wagner and Rick Stearns, and heard a pep talk from the candidate.

After the end of the primary season in June, the Kennedy campaign was talking about a major effort to win Carter delegates over to their side. But so far, this has not amounted to much.

For a few weeks, the Kennedy people concentrated on keeping their delegates informed of the evolving strategies for platform and rules fights at the convention. But except for a few "Dear Delegate" form letters and a late-starting, small-budget telephone campaign, the Kennedy workers have not made much visible effort to win over Carter-pledged delegates.

Kennedy's strategy for winning the nomination still rests on the vague hope that he can win victories on rules and platform fights during the first two days of the convention. This, in turn, would prompt a massive mutiny and lead hundreds of Carter delegates to switch to Kennedy on the third day, when the presidential balloting occurs.

The key test will come early on Monday, Aug. 11, the convention's opening day, when the Kennedy forces plan to mount a floor fight against a proposed party rule that would bind delegates to vote for the presidential candidate they were originally pledged to support.

Polls of the delegates indicate that some Carter backers do not agree with the rule forcing all delegates to vote automatically in accord with their pledge. But the polls also show that most Carter delegates, and some Kennedy supporters, now intend to vote for that proposed rule. If they do, Kenndy and the various dump-Carter activists will be out of luck.

Democratic Chairman White, a Carter stalwart, has been complaining to all who will listen that the Kennedy people want to consume so much convention time with their various rules, platform and credentials fights that the convention might spill over into a fifth day.

However, top operatives from the Kennedy and Carter campaigns have been meeting together to work out an agenda that fits the standard four-day format. And there are some indicatitons that compromises can still be developed on many platform planks, including the economic language -- a pledge that Carter will take no step that would increase unemployment -- that is now Kennedy's chief policy concern.

Carter's strategy is to keep his delegates committed and to be prepared to squelch whatever floor challenges Kennedy makes. Carter's campaign aides accuse Kennedy of being a sore loser who is trying to change the convention rules because he lost in the primaries.

Tom Donilon, Carter's delegate coordinator, said he has found no slippage to Kennedy among Carter delegates on the nomination, but that some delegates are confused on the rules issues.

"Kennedy people are putting out the big lie strategy on the theory that the bigger the lie is the more people will believe them," Donilon said.

If delegate interviews are any indication, Donilon and company are succeeding in convincing Carter delegates.

"We've got to keep telling our delegates that Jimmy Carter has run the most open presidency in history," said Joe Murphy, the Washington state Democratic chairman and a Carter delegate. "The biggest thing we wanted to learn here is what to do about Kennedy spreading the big lie -- that this isn't an open convention."