Americans continue to have confidence in themselves and their system, but they are increasingly disenchanted with the overall state of the nation. In particular, public trust and confidence in the federal government have dropped significantly over the last four years.

These are among the conclusions of a new survey that spells out challenges - and risks - for Jimmy Carter and his administration.

The national survey, the latest in a continuing series from Potomac Associates in Washington, portrays Americans as ready for change and disapproving of "inaction in government or leadership by veto." Carter, in this reading, must be willing to take risks if he is to match the public mood.

"If for any reason Jimmy Carter were to construe his presidential role as that of caretaker, our research would prompt the prediction right now that - all party considerations aside - we would expect to have a new President-elect fours years from now," the report states.

The public perception of the federal government, a central theme in the Jimmy Carter-Gerald Ford presidential campaign, is nearly uniformly unfavorable, according to the survey data. In only one category of federal activity - the judiciary - was there an improvement in the public's trust and confidence rating over that of four years ago. All others showed "significant decreases."

Confidence in the way the federal government handled domestic matters continued to drop from previous samplings in 1974 and 1972. But the sharpest drop in federal performance came in the handling of international problems. Public atttitudes in this area showed a "startling" decline, in just the last years.

"Considering that foreign policy in the last several decades normally has been considered a source of strength for most administrations, the Johnson administration's Vietnam policy being the major exception, this must be taken as an expression of serious reservations by the public about the Ford-Kissinger performance," the study says.

Both the legislative and executive branches are viewed with notably greater criticism than in 1972. Ford did, however, apparently succeed in redressing the "shocking decline" in public approval of the way the White House was operating when he took over from Richard M. Nixon.

While the President did not recover all the lost ground from the survey of 1972, the public did beleive his White House was functioning substantially better. That factor, the data concluded, may have helped account for the closeness of the election.

In the overall ratings, Americans expressed the strongest faith in themselves. "The judgement of Americans on this issue was virtually unanimous," the report says, "with all elements of the population showing high levels of trust and confidence in the people as a whole."

That confidence remains unshaken despite the turmoil and scandals of recent years, and is not subject to wild gyrations of public mood. Americans view themselves and their system in "remarkably stable" terms.

What comes through the data is a sense of a highly mature citizenry, assessing the scene around them with considerable discretion and selectivity. A public, too, that in the words of the report reacts to what it preceives "with an impressive degree of realism and good sense in deciding where their trust and confidence should be given - or withheld."

A paradox, however, exists. While Americans continue to be rather well satisfied with their personal lives, they take much less comfort in the general state of their nation. The split between their perception of their personal world and the world "out there" persists. It is in that area that Carter faces his greatest challenge, the report suggests.

He comes to office at a time when national leaders have been unable to stir the kinds of enthusiasm and imagination of the past. And although Americans are pragmatic about their society and government, they also, as the report says, "live by their dreams." As posed by the study, the challenge for Carter is to cut the "subtle and confused web" that people do not know how to unravel.

"In a word that poses ever more complex questions and problems," the report says, "it is a source of major frustration to realize that we probably cannot obtain clear and final answers to many of our most pressing difficulties. For many individuals in today's world, despairing of solutions, it is enough to cope. Such attitudes as these may account for disturbingly low voter participation, and other evidences of apathy that could portend more serious political alienation in the future."