The American people differ sharply with President Reagan's proposed spending priorities for fiscal 1987, with a majority favoring cuts in the Defense Department in order to reduce the federal deficit, and nearly two-thirds opposing cuts in social programs for that purpose, according to a Washington Post-ABC News national opinion poll.

The poll showed that by 68 percent to 30 percent, however, the public agrees with the president that taxes should not be raised to reduce the federal budget deficit.

In the foreign policy arena, Reagan got his best rating ever -- a 75 percent approval to 21 percent disapproval rating -- for the way he is handling relations with the Soviet Union.

The public is far more sanguine about superpower relations than it was a year ago, with 92 percent saying things are getting better or staying the same, and with optimism on the rise since the summit last November.

They also appear to have a favorable impression of Soviet leader Mikhail Gorbachev. By 63 percent to 27 percent, the American people give him a favorable rating. By 60 percent to 32 percent, they say they think Gorbachev is serious about making progress on arms control, and by 74 percent to 22 percent, they say they favor his proposal to eliminate all nuclear weapons by the year 2000.

On the perennial guns-versus-butter budget debate, the poll shows that attitudes have undergone a dramatic swing since Reagan took office five years ago. Of 10 domestic programs surveyed, support for increased funding of all of them is greater today than it was five years ago.

Support for increases in funding for the military has dropped precipitously, from 72 percent five years ago to 22 percent today (this response was to a question not tied to deficit reduction). Reagan's budget calls for an 8 percent increase, after inflation, in funding for the military. Reagan plans a nationally televised speech in late February as part of an effort to drum up support for his defense budget.

Reagan's domestic spending program, which calls for cuts in Medicare, Medicaid and student loans, among other domestic programs, will run into stiff opposition from the public. The percentages of Americans who want funding for those programs to increase or stay the same are: Medicare, 96 percent; Medicaid, 91 percent, and student loans, 79 percent.

Overall, 64 percent oppose cuts in social spending to reduce the deficit, while 56 percent support cuts in military spending for that purpose. The 68 percent who oppose a tax increase hold a view that is slightly less popular than it was at the time of Reagan's second inauguration, when 79 percent of Americans opposed a tax increase.

The telephone survey of 1,504 adults, taken from Feb. 6 to 12, also offers a grab bag of findings on a variety of issues:

*By 83 percent to 16 percent, Americans say they think that the manned space shuttle program should continue despite last month's explosion of the Challenger. Seventy percent say they think that civilians should be included in future flights, although only 39 percent said they would like to ride on the shuttle, a decrease from the 48 percent who expressed an interest in riding the shuttle in a Media General-AP poll taken last July.

*Vice President Bush is the leading choice of his party for the 1988 presidential nomination, with support from 43 percent of those in the survey who described themselves as Republican or Republican-leaning. Other Republican choices (in response to a list of names read to those surveyed): former president Gerald R. Ford, 13 percent; former Senate majority leader Howard H. Baker (R-Tenn.), 12 percent; Senate Majority Leader Robert J. Dole (R-Kan.), 10 percent; Rep. Jack Kemp (R-N.Y.), 8 percent; former U.N. ambassador Jeane J. Kirkpatrick, 4 percent; television evangelist Pat Robertson, 2 percent, and former defense secretary Donald Rumsfeld, 1 percent.

*Sen. Gary Hart (D-Colo.) is the leading choice of his party for the 1988 presidential nomination, with the backing of 38 percent of those who called themselves Democrats or Democratic leaners. Next, from a list of names read to the respondents, came New York Gov. Mario M. Cuomo with 17 percent; Chrysler Chairman Lee A. Iacocca, 15 percent; Sen. Bill Bradley (D-N.J.), 10 percent, and Sen. Joseph R. Biden Jr. (D-Del.), 1 percent.

*Fifty-four percent of Americans say they believe women should be allowed to have an abortion on demand, an increase over the 40 percent who held that view five years ago. In addition to those who support unlimited abortions, 34 percent say they believe abortion should be legal under some circumstances. Men and women have nearly identical views on the subject.

*By 53 to 41 percent, Americans say they think it is a bad idea for the United States to help overthrow procommunist governments.

*Reagan enjoys his greatest overall popularity with the youngest voting age group, the 18- to 30-year-olds, who approve of his job performance by 71 percent to 27 percent. That approval, however, does not amount to an endorsement of Reagan's philosophy of less government. The same group is the only one that supports increased governmental activism, by 50 percent to 48 percent.

*By 49 to 45 percent, the public says it would prefer to see the Democrat in their district win the congressional election over the Republican, yet by 46 percent to 40 percent they say they think the GOP will do a better job coping with the main problems facing the country. How Post-ABC Poll Was Conducted

The Washington Post-ABC News public opinion poll on attitudes toward current public issues was conducted by telephone in the continental United States from Feb. 6 to Feb. 12. In all, 1,504 persons, selected at random, were interviewed.

The sample was adjusted slightly to conform to Census Bureau figures for the overall population with regard to age, education, race and gender.

Theoretically, in 19 cases out of 20, a poll of 1,504 persons is subject to a margin of sampling error of about 3 percentage points. Figures based on large subgroups, such as women, have a slightly higher margin of sampling error. Polls have other potential sources of error besides sampling procedures.