The year's most burtal demonstration of Jimmy Carter's unpopularity has transformed Sen. Edward Kennedy's simple desire to salvage personal and family honor into a difficult personal choice that divides his loyal supporters into passionate camps.

Before the June 3 primaries in a heart-to-heart conversation with a close family friend, Kennedy laid bare this deepest hope: to emerge from his often humiliating pursuit of Carter with restored honor. But having humiliated President Carter with five out of eight primary victories, merely withdrawing from active battle with the family banner honorably flying is not enough. Kennedy himself made that dramatically clear after meeting with the president yesterday.

Many of his staunchest backers want him to carry that banner right into Madison Square Garden to test the miracle machine. The senator's refusal to accept telephone calls from the president Tuesday, the sharpest snub to a president since George B. McClellan turned Abraham Lincoln away from his door in 1861, signaled his own frame of mind. Kennedy finally returned Carter's call Wednesday and agreed to an Oval Office meeting on Thursday.

Cool-headed professionals within the Kennedy camp feel the time for fighting is finished, with fratricide, not a Kennedy victory, the likely yield in Madison Square Garden. That is the view of the highly respected Rep. Paul Simon of Illinois, one of Kennedy's most important early supporters. "If he called me to ask whether to stick it out or heal the wounds, I'd say heal the wounds," Simon told us.

To Teddy Kennedy's inside aides and advisers, that is a counsel of defeat they spurn. With their emotions at fever pitch following the senator's best Tuesday all year and Carter's cheerless "victory" party here Tuesday night, ardent Kennedyites are spoiling for more fight.

Former governor Patrick J. Lucey of Wisconsin, a top Kennedy adviser, called the senator Wednesday morning but found him asleep. His relayed message: "Stay in all the way." Many Kennedy backers around the country agreed. "The time to regroup is after the nomination has been made at the convention," Mayor Richard Fulton of Nashville told us. Don Hanni is Democratic chairman of Ohio's Mohoning County (Youngstown), where Carter's name means runaway inflation and recession-style unemployment. After his county backed Kennedy in a landslide, Hanni said he wants Kennedy "to go all the way to the floor [of the convention] and let's see what happens."

Although Carter captured Ohio by a comfortable margin, he lost blue-collar Democratic Cleveland and Toledo, as well as Youngstown, to Kennedy. In Ohio as in the nation, where Democratic presidential nominees should be strongest, Jimmy Carter was weakest. That invites supporters like Don Hanni to stick with Kennedy.

But such lingering dreams are outweighted by the nightmare of party civil war for most party leaders and Democratic candidates this fall. Kennedy supporters are included in both categories.

"When this primary season ends," a top Kennedy backer in Cleveland running for local office told us last week, "the split has to end or I'll go down." That view is largely shared by at least one member of Kennedy's political high command: Joe Crangle, the veteran party leader in Buffalo.

Non-Kennedy Democrats are getting frantic in their desire for Kennedy to stop. "I need a presidential nominee at the top of the ticket who has not been mortally wounded," said Harold Pachios, the former Maine Democratic state chairman now running for Congress. An important party leader in Congress says privately that if Kennedy becomes vulnerable to charges of contributing to Reagan's election, "he will write himself out of his party."

Such emotions were pallid compared with the concealed fury within Jimmy Carter's White House. When word got around early Wednesday that Kennedy had initially declined the presidential olive branch in the form of not one but two rejected Carter telephone calls, one presidential adviser blurted out: "Teddy is a spoiled little rich kid who can't get what he wants."

Carter's aides do not intend to let Kennedy's cold shoulder edge them into public scolding -- not yet, anyway. Carter has confided to congressional leaders that the senator needs time for "decompression" and "calm thought," after which he will surely see that both his own and his party's interests argue for accepting the olive branch.

But Kennedy clearly surpassed his expectations on super Tuesday, enlarging his earlier, limited ambition to rehabilitate the Kennedy name by a gallant race after his self-destructive start. If he now really believes in the impossible dream of deposing Carter, the Democratic Party may be headed for a convention rivaling 1968 and 1972 in divisive turbulence.