Democratic governors said yesterday they would stand or fall with President Carter, while two possible 1980 challengers - Sen. Edward M. Kennedy (D-Mass.) and California Gov. Edmund G. (Jerry) Brown Jr. - offered conflicting advice on how Carter should respond to the Proposition 13 tax revolt.

With Brown adding his voice to the rest, about 30 Democrats attending the National Governors' Conference here unanimously approved a general resolution backing Carter's leadership and promising to help him with what many of them were calling a "recalcitrant" Democratic Congress.

Outside in the corridor, however, Brown complained that federal policies punish states such as his that cut their own taxes, and warned that a "tidal wave" of resentment was building against "traditional Democratic spending programs."

An hour later, Kennedy went before a plenary session of all the governors to make his case for one of the biggest of those programs - a national health insurance plan.

To a tattoo of somewhat skeptical questions, he insisted that Carter's proposal to inaugurate national health insurance in a series of slow steps over the next several years risked a voter rebellion against the rising cost of private medical care that would make the Proposition 13 tax revolt seem a mere ripple on the political sea.

In a long day of political posturing and policy discussion that began with party breakfasts and ended with a New England clambake, the most substantive development was the apparent feeling by most Democratic governors that the time had come for a show of support for the embattled president.

Many of them have been highly critical of paticular Carter policies in their states, and they repeated those criticisms here. But retiring Govs. Reubin Askew of Florida and Mike O'Callaghan of Nevada told the closed-door Democratic breakfast that they had more access and influence with Carter as a group than they had enjoyed with his Republican predecessors. A generally worded resolution of support for the president offered by West Virginia Gov. John D. (Joy) Rockefeller IV. went whistling through without a dissent.

But it masked continued apprehension among the Democrats about the impact of Carter policies on their political futures. Colorado Gov. Richard D. Lamm and others running this November told Rockefeller privately they resented his offering the resolution without advance notice. But with presidential assistant Tim Kraft and Democratic National Chairman John White in the room watching, they did not protest it.

North Carolina Gov. James B. Hunt Jr., who succeeded O'Callaghan as head of the Democratic governors' caucus, told reporters that the feeling was that "there are problems, sure, but this is our administration and if the president is hurt, we're all hurt."

Hunt also said the Democrats believe that Carter "has turned the corner" on some of his problems. "People resent all the problems being laid to the president." Hunt added, "when it is the Congress and the special interests that have blocked action."

His criticism of the Democratic-controlled Congress was echoed by many state executives of both parties, as the governors worked through preliminary discussions of the policy positions they will adopt at today's closing sessions.

But Brown, as usual, was doing his own thing, as he paused here for less than 24 hours between a fund-raising stop on Long Island to benefit his re-election campaign and a visit to Maryland to boost the candidacy of Ted Venetoulis - a 1976 Brown-for-president backer who is seeking the Democratic gubernatorial nomination.

Brown's message was that the taxpayer revolt that broke out in his state with the passage of Proposition 13 in June "could well unravel the Democratic coalition" unless the federal government responds to "the risking wrath of the middle class" without abandoning its "Historic commitment to the poor and the dispossessed."

Kennedy a leading advocate of national health insurance, urged the governors to support such a program as a way to control inflation and promote competition in the health-care industry.

But the governors, who twice in the last two years have voted against resolutions approving national health insurance expressed skepticism and outright opposition.

Kennedy argued that a national program would mean a lower rate of cost increases because it would force states to budget health-care programs years in advance. But Gov. Otis R. Bowen of Indiana, a physician, said he doubted that a "federally dominated program will be better and cheaper than what it would replace."