Although Americans welcome efforts by President Reagan to keep federal spending under control, and they want substantial cuts in a number of programs, prospects for early adoption of Reagan's economic program are not encouraging.

Essentially the president will encounter a twofold problem, according to this latest Harris Survey of 1,250 adults nationwide.

By 67 to 28 percent, a majority of Americans rejects making "cuts in both spending and taxes at the same time," and opts for "no tax cut until federal spending has been cut in a major way." Even those who voted for Reagan give spending cuts a priority over tax reduction by 65 to 33 percent. But partly because of his campaign commitment to a 10 percent tax cut for three years running and the deep conviction of his supply-side economic advisers that tax relief must be sustained and continuing over several years, Reagan has been unyielding in his insistence on spending cuts and tax cuts simultaneously.

Despite the general public commitment to cut federal spending, people actually are highly selective about just where the cuts ought to be made. For example, cuts in the comprehensive employment and training program, a favorite of liberals, would be favored, 62 to 31, but cuts in the school lunch program, another favorite of liberals, are opposed, 63 to 35. Similarly, cuts in veterans' benefits, long a favorite of conservatives, are opposed, 66 to 31, but cuts in general revenue-sharing with the states and localities, another favorite of conservatives, are favored, 61 to 30.By calling for cuts across the board, and in amounts well over the $18.8 billion the public is willing to accept, Reagan risks obtaining far lower cuts in spending than he has called for. This, in turn, could be viewed as inability to deliver on his promises.

In addition, if the Democrats are successful in saving the budgets for such popular programs as aid to primary and secondary education, Medicaid and Medicare, or school lunches, they will gain politically at the Republicans' expense Significant, but of ten overlooked in this upcoming battle between the president and the Democrats in Congress, is the fact that Reagan must obtain a majority in both houses to have his programs passed, whereas the Democrats need only win in the House of Representatives to prevent a cut in a specific program. The tactical advantage clearly is with the Democrats.

However, it also is important to point out that the last two occupants of the White House who at times found their programs mired in Congress -- Jimmy Carter and Gerald Ford -- were not effective communicators with the public. As a result, both presidents had trouble taking their case over the heads of Congress directly to the American people. Reagan is something else again. By 77 to 17 percent an overwhelming majority gives him positive marks on inspuring confidence in the White House. For the moment, at least, he is presiding over a very popular administration, whereas the Congress has remained a relatively unpopular institution for many years now. So the instinct of Americans will be to sympathize with the president rather than with Congress. In addition, Reagan has amply demonstrated that he is one of the more effective communicators to occupy the Oval Office in recent times.

The outcome of this confrontation is likely to depend, first, on the extent to which Democrats can hold their ranks and block those proposed budget cuts that are unpopular and second, on the extent to which Reagan can go over the heads of Congress to the people. If Reagan can make an issue out of Democratic intractability on cuts that are popular, then he could well finich on top.