President Carter's chief domestic affairs adviser today defended the president's energy policies before a meeting of Democratic governors, saying the energy crisis was "on the road to a solution."

Stuart Eizenstat said the administration has established a "clear, understood" fuel-pricing policy, a fuel-conservation program and a workable plan for the development of alternate energy sources. He did not elaborate.

Several of the president's energy and economic advisers have proposed major changes in those policies, including ending oil price controls and scrapping the gasoline allocation scheme that has worsened shortages in urban areas.

Eizenstat told the governors that the administration is working on a plan to issue regular reports on fuel supplies across the nationa, reports that he said will have the "credibility of the consumer price index."

In a June 28 memo to Carter, Eizenstat noted that "the continuing problem of conflicting signals and numbers" from the Department of Energy persists. "The DOE allocation formulas are now coming under particularly heavy attack."

And he referred to "enornous credibility and management problems" at DOE that "equal in public perception those which State or Defense had during Vietnam (whether fairly or not)."

Today, however, he did not appear to emphasize the strategy outlined in the memo calling for the administration to use the Organization of Petroleum Exporting Countries (OPEC) as "a clear enemy" to mobilize support for Carter's energy policies . . .

He told the governors only that "our country should not stand for any continued vulnerability to OPEC.

And today in Washington, administration officials sought to downplay that memo. One Carter Assistant termed the memo "a little silly" in its rhetoric, and suggested that it was prepared by underlings while Eizenstat was preoccuipied with other matters.

In an interview here, Eizenstat said the nation's crisis mood over energy supplies, about which the governors were warned, will probably make it easier rationing program quickly.

Eizenstat said the president, who was continuing his meetings at Camp David on domestic problems, "is not running out of time" in which to salvage his low standing in public opinion polls.

Eizenstat said that Carter "will come out swinging" after the Camp David sessions.

Meanwhile, the Democratic governors were warned that the Untied States is a "society preoccupied with energy and inflation." They also were told that the coming years "may not be much fun" for the nation's governors.

Worry about the gasoline shortage and anxiety about increasingly angry voters dominated nearly every discussion at the gathering of 21 Democratic governors that preceded Sunday's opening of the national governor's conference.

Pollster Peter D. Hart was asked for a reading of the mood of the nation. He told the governors that people think "things are generally in chaos."

Hart said three-quarters of the public see the president as ineffectual, and the overwhelming sense of the country "is that we don't know where we are heading."

Picking up on that, Rep. Morris K. Udall (D-Ariz.) warned the governors that, "This country faces a major wrenching transition. It may not be much fun being governor during these wrenching years . . ."

Those Democratic governors who arrived here today after meeting Friday night with the president at Camp David said the mood of their session with Carter was optimistic and that he has not made up his mind on any new energy proposals.

"I bring you a great message of hope," Gov. James B. Hunt of North Carolina told the governors, referring to the meeting with the president. Hunt, chairman of the Democratic Governors' Association, did not specify why he was hopeful.

Gov. Julian Carroll of Kentucky told reporters that there was a lengthy discussion with the president Friday night about an "energy management board," which Carroll said would be made up of energy experts and empowered to make immediate decisions on key energy problems, including gasoline allocation.

The governors were told by public opinion expert Richard M. Scammon today that the country looks to the president, not to the governors, for leadership in times of crisis.

Scammon, director of the Eelctions Research Center in Washington, D.C., said that what the people now perceive when they look at Carter is "command freeze," the inability to act under pressure.

To solve this image problem, Scammon told the governors that the president must "do something positive that gives people the impression . . . that they can say, 'To hell with OPEC.'"

Hart said that the governors, as well as the president, now face an angry public that doesn't seem to know what it wants. He said that his polls show that 16 percent of the country wants to break up the big oil companies, while 9 percent think that idea is the worst thing that could be done to alleviate the gasoline shortage. CAPTION: Picture, Members of the National Governors' Conference meet with reporters in Louisville after returning from Camp David. From left are Govs. Julian Carroll of Kentucky, Dixy Lee Ray of Washington, Ella T. Grasso of Connecticut, James B. Hunt of North Carolina, Otis Bowen of Indiana, George Busbee of Ga. and Brendan Bryne of N.J. AP