When a distressed Gov. Jim Hunt of North Carolina visited the White House Feb. 28, he warned Jimmy Carter how low the president's stock had fallen here - an appraisal with orgins and implications going well beyond the borders of North Carolina.

Hunt's polite warning only suggests the blunt assessment here. "If Carter were running against Jerry Ford right today," one veteran Democratic politician told us, "there is no way he could carry North Carolina." More immediate is widespread Democratic fear that the Carter connection could reelect conservative Republican Sen. Jesse Helms and unseat three Democratic congressmen in 1978.

Specific reasons are the federal governments unrelated drives to curb tobacco smoking and force further - and highly questionable - racial integration at the respected University of North Carolina. Thus has the Carter administration joined together two disparate lobbies in this state: tobacco and the university. Behind this lies President Carter's failure to remember one campaign pledge and his too faithful fulfillment of another.

The remembered pledge promised Cabinet government without White House interference. The antismoking campaign and, to a lesser extent, the university integration push are creatures of Joseph Califano, who runs the Department of Health, Education and Welfare without much presidential supervision. But in giving Califano his lead, the president has acquiesced in more federal interference in the affairs of local government and individuals - not less, as promised.

That is the sad conclusion of Hunt, who, unlike many southern governors, likes and admires Carter. An early Carter-for-president backer, Hunt told us the president has talked to him of the terrible burden of foreign affairs. "With all that on his mind," Hunt said, "I think the president has gotton away from some of the things he started with."

The governor, no state's-right Dixiecrat, is a moderate liberal with national aspirations. Nevertheless, he believes the troubles in his state reveal the federal government's obsession for a centrally directed statist society. If being for smoking and against integration were not politically reprehensible, Hunt might take his case to the nation.

Hunt has tried dealing directly with Califano, cornering him for 15 minutes at a fund-raising dinner in Atlanta as well as conversing over the telephone. (SECTION) uperbureaucrat Califano cooed his understanding of the governor's problems. But nothing changed. Matters had to be taken up with the president.

So Hunt (in Washington for the winter governors conference) and Sen. Robert Morgan visited the president Feb. 28. Carter was sympathetic to the tobacco and university problems, and the governor returned here voicing optimisum; the rhetoric from Washington would soon change, he promised.

In truth, most everybody else involved is pessimistic that anything will change. Nobody at the White House has been able to control Califano, who is perceived there as a grandfather. The president told Hunt and Morgan he would talk to Califano. But Vice President Walter Mondale - Califano's friend, ex-neighbor and political patron for the Cabinet - interjected to say he would handle that unpleasant task.

Relying on the vice president to curb a Cabinet member running counter to a Cabinet member running counter to the president's stated philosophy suggests the administration is malfunctioning. At this writing, nearly a week after Mondale's promise, the "no smoking" campaign is still lit up at HEW.

If that continues, Democrats will try to salvage the 1978 North Carolina election by pinning big brotherism on Califano while isolating Carter. Democratic leaders here take malicious delight in mispronouncing the secretary's name while attacking him. One party strategist invariably drawls out "Cal-uh-fran [rhymes with pan]-o," adding the "r" with unmistakable contempt.

But isolating the president from his own administration is difficult. At one Cabinet meeting, Secretary of Commerce Juanita Kreps (a North Carolinian and longtime Duke university official) protested HEW activities in her old state. Califano responded with customary vigor. That much is certain. What Mr. Carter then said is in dispute, but one version widely circulated here has the president backing Califano. Ture or not, the story has taken on a life of its own.

The president will be at Winston-Salem March 17 for a hastily arranged speech (on defense matters only, scheduled without anyone's consulting Hunt or other North Carolinians). But what will really determine his political future here are the tobacco and integration campaigns. Without any change, Democratic candidates here will treat Carter like a plague this year. More important, fresh doubt will spring up as to whether he yet firmly grips the reins of government.