Americans are showing dramatic shifts in their perceptions of President Reagan, with a majority tending to view the president as siding with the wealthy and being far more sympathetic to big business than to labor, according to the findings of a new Washington Post-ABC News public opinion poll.

Furthermore, at a moment when the Reagan administration is sounding a call for further reductions in social programs, the public is moving in the opposite direction, with a strong plurality saying that Reagan is going too far in his plans for such cuts.

Overall, Reagan remains personally popular, but he and his economic programs are subject to a skeptical appraisal that did not exist just a few months ago. He is losing support among older Americans and among many Democrats who had backed him earlier. Black Americans, always strongly opposed to Reagan, are almost unanimous in their disapproval.

Instead of being optimistic about the nation's economy now that Reagan's tax and domestic spending cuts are in place, most Americans are decidedly pessimistic. Only one in eight among those polled says he feels that the economy is getting better. The rest are evenly split between those who say it is worsening and those who say it is staying about the same.

The glow seems to be fading in other ways as well. Where some Republican leaders have been citing poll findings as evidence that the GOP is becoming the majority party, the new Post-ABC News poll shows affiliation with the Republican Party to be declining slightly in recent months, and affiliation with the Democrats increasing.

In one vital current issue, military spending, the public continues to support Reagan strongly, according to the poll. Asked whether Reagan is going too far in his plans to increase military spending, not far enough, or whether his planned increases are just about right, 52 percent say his proposed increases are just about right. Another 19 percent say he isn't going far enough, and only 23 percent say the proposed increases are too large.

A total of 1,501 adults were interviewed in the new poll, which was taken by telephone from Sept. 14 to Sept. 20. A number of the questions were the same as ones the Post and ABC News have been asking since Reagan took office, so clear trends may be noted.

For example, when Reagan announced plans for a 30 percent across the board tax cut and spending cuts of some $40 billion in February, this question was asked: "Overall, would you say Reagan cares more about serving poor and lower income people, middle income people, upper income people . . . or would you say he cares equally about serving all people?"

At that time, 23 percent said Reagan cared more about upper income people, and 64 percent said he cared equally about serving all the people. In April, when the same question was asked, 29 percent said he cared more about upper income people and 58 percent said he cared equally for all the people.

Reagan won almost all he asked for from Congress, with a three-year, across-the-board tax cut of 25 percent and budget cuts totaling about $40 billion. But with that political victory, he also apparently altered perceptions of himself. In the new poll there is a striking shift: today 52 percent say Reagan cares more about serving upper income people and 35 percent say he cares equally about serving all people.

Along the same line, the Post-ABC News poll contained this question, which had not been asked previously: "If you had to choose, would you say Reagan is more sympathetic to big business or to labor in the United States?" A total of 78 percent say "big business," 12 percent say "labor," and 10 percent express no opinion.

On Thursday night the president is to address the nation on television. He is expected to outline a request for further budget cuts and appeal to the public for support. As he does, he will be speaking to a citizenry that may not be as receptive to such cuts as it was in the spring and summer, according to the poll's findings.

Question: "Some people say that Reagan is going too far in his plan to cut back or eliminate government social programs; others say his proposed cuts are just right, and still others say he is not going far enough. How about you: which of those views comes closest to your own?"

In April, when Post-ABC News interviewers first asked that question, the public tended to side with Reagan's cuts. Forty-two percent said the cuts were just right, 33 percent said the president was going too far, and 18 percent said he wasn't going far enough.

The new poll, taken just as many of those cuts are about to take effect, shows a sharp reversal. Forty-seven percent say Reagan is going too far in cutting social programs, 30 percent say the cuts are about right and 19 percent say the president isn't going far enough.

Overall, 61 percent of those interviewed say they approve of the way Reagan is handling his job as president, a figure that has been just about constant since March, with the exception of a sharp burst of approval following the assassination attempt against him at the end of that month.

At the same time, however, the new poll shows fewer people saying they are undecided about Reagan and more saying they disapprove than at any time since his election. In all, 34 percent give Reagan a negative job rating, a six-point increase since July.

At the onset of his term, Reagan's strongest supporters were older people. Beginning in May, however, when he announced plans for cuts in the Social Security program, successive polls have shown that support eroding. In February, people 61 and older said they approved of his handling the presidency by a 71-to-12 ratio. Now the figures are 51 to 39.

Blacks, on the other hand, expressed disapproval from the beginning. In February, he received negative ratings from blacks by a two-to-one margin. Today that figure has jumped to five to one.

The poll strongly suggests that the new discontent is tied to concern over the economy. Reagan has maintained that it is too soon for sharp change to have occurred. But the public, at least according to the poll, hasn't noticed any change for the better, either in the national economy or in their own finances, or in the overall employment picture.

If anything, the public appears slightly more pessimistic now on all three counts than it has recently, according to the poll. There is a marginal increase in the number saying the economy is not getting better, in those saying they have trouble paying their own monthly bills, and in the number thinking that next year won't be any better for themselves than this year has been.

On employment, Reagan was given a somewhat positive rating in April, when 38 percent told Post-ABC News interviewers that they approved his handling of that problem and 29 percent said they disapproved.

That rating has also switched: now it is 40 percent approve and 44 percent disapprove. As might be expected, that shift is most pronounced among less-educated Americans, the ones who are usually most affected by problems in the job market. How the Survey Was Conducted

A total of 1,501 people were interviewed by telephone Sept. 14-20 in The Washington Post-ABC News poll on attitudes of Americans toward President Reagan and other issues. Theoretically, figures based on that many interviews are subject to a sampling error of about 2.5 percent in either direction 95 percent of the time. Figures based on subgroups are subject to a slightly higher theoretical margin of error.

The latest available U.S. census figures on age, sex, education and race were used to adjust the sample slightly so that it matches the overall population in those characteristics.