When the soothsayers of public opinion on President Carter's national energy plan whisper in his ear, they could begin with the bad news.

The public is against most of the crucial proposals in President Carter's energy package. The people do not want a conservation tax on gasoline. The people are opposed of his "gas guzzler" tax on large automobiles. They do not like his plan to let "new" oil rise to match the world price. They do not even agree with his attempts to halt development of fast-breeder nuclear power plants.

Now here is the good news. Mr. President - a majority of the people want Congress to enact the Carter energy program.

These conflicts messages, derived from a new public-opinion study by Cambridge Reports, illustrate once again that the general public is capable of embracing contradictory positions just like some politicians. But the study also describes a delicate political contour of the Carter presidency - making policies that are offensive to folks who voted for him last year, but appealing to those who didn't.

The Cambridge survey, which conducted 2,400 personal interviews during the last two weeks of May, was commissioned by Westinghouse Electric Corp., but Washington policy makers will study it closely because the president of Cambridge Reports is Patrick Caddell, the unpaid political adviser to President Carter. Caddell did not work personally on the energy survey, but it is reasonable to assume that he will familiarize the President with its findings.

In broad terms, the contradictory signals from the public make sense in this way:

The strongest opposition to Carter's specific energy measures, at least the proposals which mean higher taxes, comes from the traditional Democratic constituencies which elect him last fall - the poor and less educated citizens, the blue-collar workers, the blacks. Conversely, most of these proposals win support among professional and managerial ranks - the better, educated and more affluent citizens who voted for Gerald Ford.

But when the Cambridge survey asked citizens for their overall view on Carter's energy plan regardless of dislike for some specifics, the traditional Democratic voters give Carter a vote of confidence - switching to support for the President's general leadership on the subject. In all, 51 per cent said they want Congress to accept the plan, compared with 25 per cent who want it rejected and 23 per cent who don't know. This contrasts with these views on specifies:(TABLE) Gasoline tax(COLUMN)34%(COLUMN)59(COLUMN)7 Guzzler auto tax(COLUMN)40(COLUMN)50(COLUMN)11 Halt breeder reactor(COLUMN)23(COLUMN)32(COLUMN)46 Lift "new" oil price(COLUMN)36(COLUMN)45(COLUMN)19(END TABLE)

The general public is much more sympathetic with elements of Carter's plan that do not suggest personal economic pain or sacrifice. Tax credits for home insulation and solar power, for instance, are supported by 76 per cent, opposed by 17 per cent.

A substantial majority wants to encourage the use of coal and also to build more nuclear power plants, the two energy supplies that are crucial to meeting Carter's goals for 1985, if it can be done without environmental damage.

In the short run, the political message seems to be this: Carter's personal popularity and the continuing confidence voters give added bouyancy to his energy package - even though a lot of those folks are against what he is proposing.

In the long run, however, the political effects of the energy plan may be more dramatic. The general results of the survey suggest that Carter's energy proposals are effective in reaching out to the new constituency that Caddell emphasized in the celebrated memorandum on political strategy that leaked out last winter - the white collar and professional the college-educated voters.

"This is the largest rising group in the population," Caddell wrote. "It must be attracted in significant numbers if Democrats are to be successful in the future."

But what attracts the affluent about energy conservation are the very elements that antagonize the working class and poor. If Congress enacts all of those measures for President Carter and raises the price of cars and petroleum products, not to mention the general cost of living, the impact will offer an interesting test of whether Caddell's game plan produces votes - or loses them.

The proposed "gas guzzler" tax, which is intended to penalize large and inefficient cars, illustrates this conflict.

Among professional people surveyed, the idea wins support, 50 to 39 per cent. Among skilled blue-collar workers, it is rejected, 52 to 36. The very poorest families under $4,000 income are against it, 47 to 34, while the most affluent over $25,000 are for it, 49 to 44. Citizens with only a grade-school education are opposed, 55 to 27: college graduates are for it, 58 to 38.

Issue after issue in the Cambridge survey illustrates that the energy debate is very much an argument between the different social classes. The Carter proposal for allowing "new" oil to rise to the world price is opposed, for instance, in every income group under $25,000 - but supported by the most a fluent. Democrats oppose the idea, 47 to 34 per cent; Republicans support it, 44 to 38.

The shorthand explanation is that President Carter's general approach, stressing conversation of energy more directly than increased production, appeals to the environmentalist concerns to younger voters and the affluent, suburban, well-educated classes. The working class and the poor are more worried about the jobs and the high prices.

Skepticism about conservation proposals tended to increase as the survey moved down the income and social scale. By 53 to 36 per cent, the public believes that they as individuals cannot do much to save on energy - but that there are others in the society who ought to do the conserving. People with low incomes were especially pessimistic.

"To some extent," the report noted, "this clearly reflects the true situation since it is likely that wealthier Americans do use propotionately more enrergy. However, this skepticism about conservation on a large part of the basic Carter/Democratic constituency probably weakens the political basis for support of the program."

Furthermore, the general public overwhelmingly prefers the idea of conserving energy through governmnet-made rules - instead of Carter's strategy of conserving fuel by raising prices. The "rules" approach is regarded as more fair, 71 to 13 per cent.

The Cambridge survey says this "may reflect a growing feeling that it is precisely those who can most easily afford to pay who are the chief energy wasters and, thus, the only realistic method of effective conservation is by rules.

"All in all, the public seems quite confused about what to do. Although conservation is viewed as cost effective, there are serious doubts as to its effectiveness as a solution. It would seem that while a majority of the people feel that they can do something personally to conserve, they also feel there are other people who ought to be forced by rules to act before they do."

On the other side of the energy debate, the public takes very strong positions - the theme pushed by the energy industry - but it continues to insist on the environmental safeguards which the energy companies want relaxed.

For instance, 73 per cent favor expansion of offshore drilling for oil and gas, 55 per cent support nuclear power plants and 68 per cent favor the increased use of coal.

However, when the survey asked whether people want more coal burned "even if this means dirtier air," the balance swings against coal: 50 to 36 per cent. This has been a fairly consistent public attitude over several years, according to the Cambridge analysis, but the environmentalist sentiment has become somewhat weaker in recent months.

The public throws one big curve at public officials. The American people generally have much greater faith than Washington policy makers do in solar energy as a major solution to energy problems. When asked what energy source would be most important to America 25 years from now, 38 per cent chose solar energy: the same proportion chose nuclear.

When the survey asked the people being interviewed to accept the argument that solar energy will not be feasible as a major source that soon, and then repeated questions about other fuels, it found increased support for coal and nuclear power.

On several related issues, the survey found continued public hostility toward the major oil companies. For instance, 51 per cent favor a national energy corporation which would explore for the government instead of relying on private companies. A minority of 33 per cent favor nationalization of the big oil companies, while 47 per cent oppose it.