California Gov. Edmund G. (Jerry) Brown's New Hampshire Democratic campaign debut was upstaged today by the sounds of an approaching Carter-Kennedy battle and a reference by the president's mother to the possible assassination threat Sen. Edward M. Kennedy (D-Mass.) would face if he runs for president.

Brown drew some cheers from supporters among the several hundred Democrats at a party picnic here with a call to "Wake Up America" to the perils of nuclear power, budget deficits and foreign competition for jobs.

But the talk on this sun-drenched late-summer afternoon was of the political civil war that saw the state's Democratic governor reaffirm his support of President Carter while the state's senior senator, also up for reelection next year, threw his strength behind the effort to draft Kennedy as a candidate.

There was also a great deal of talk at the food stands about a cryptic remark from "Miss Lillian" Carter, the president's mother, who was his standin at the Hillsborough County picnic.

Referring to Kennedy, she said she expects him to be supporting the president, and then added: "But if he does run, I wish him all the luck in the world and I hope to goodness nothing happens to him."

The remark, which appeared to be a reference to a threat of assassination if a third Kennedy brother seeks the presidency, drew some boos. "That wasn't very nice," she said. I don't know if you're booing me or him, but don't (boo) either one of us."

But the audience was lively again as Brown -- teased by Miss Lillian as "a good-looking fellow" -- called on his party to "shake off the myths" of the past and prove that it still has "the pioneering spirit."

Brown, an acknowledged underdog in the state, made the most of his nine hours here and vowed to be back for at least five days of campaigning in October and more as the Feb. 26 primary date approaches. He attended a folk Mass in Manchester, met with several small groups of potential supporters and spoke at party picnics here and in Dover before flying back to Sacramento for the windup of the legislative session.

Aides said that Brown campaign headquarters will be opened immediately both in New Hampshire and in Massachusetts, whose primary is scheduled to follow New Hampshire's by one week.

But the New Hampshire Democrats seemed to be looking beyond Brown to the looming battle between Kennedy and Carter. At today's picnic, Gov. Hugh Gallen (D), the Carter campaign leader, praised the president as a man who had taken on "a horrendous task," and said, "I know of no one who can do better."

But Sen. John A. Durkin (D-N.H.), who spoke a few minutes later, said he knew of such a person -- Kennedy. He said, "I think he will be an active candidate soon," and urged backers of an already flourishing draft-Kennedy movement to redouble their efforts to draw Kennedy into the race.

If cheers and buttons are a measurement of support, Durkin's argument seemed to capture the prevailing hope.

Off the platform, Gallen, Durkin and Rep. Norman D'Amours (D-N.H.) all said they found the current support for Brown "pretty thin," to use D'Amours' phrase.

Durkin, who is known for his barbed tongue, said that "what is known about Brown in New Hampshire today, I don't think he'd put in a campaign leaflet. When people heard he was coming, they asked if he was coming in a canoe and if he was bringing Linda Ronstadt with him." Brown, a bachelor, made a widely publicized trip to Africa last summer with Ronstadt, a popular rock singer.

Apparently trying to play down the image that caused the Manchester Union-Leader to label him "the California snowflake," Brown took a formal, low-key tone in his public appearances.

He avoided any direct stump attacks on Carter or Kennedy, but issued a written statement questioning some aspects of the administration's handling of the Soviet troops in Cuba.

While praising Carter's "restraint" in his response to the disclosure of the presence of 3,000 Soviet combat troops in Cuba, Brown's statement questioned Carter's wisdom in having halted reconnaissance flights over the island in 1977.

Were it not for cancellation of those flights, the troop presence "might well have been detected" earlier, he said.

Brown repeated his criticism of Carter's decision to go ahead with construction of the MX missile system and told reporters aboard his campaign bus that he "doubts it makes sense" to boost defense spending "an arbitrary 3 percent" a year, as Carter has proposed.