THE SOLID victory of the administration's budget plan in the House last week was an expression of the same political sentiments that brought Mr. Reagan to the presidency; national exasperation with a federal budget and--to a lesser extent -- a federal tax bill that seemed out of control. Whether that support extends to a full endorsement of the administration's economic program remains to be seen.

Strong public support for budget control has only emerged in the last few years during which federal spending has moved outside the narrow range of around one-fifth of GNP where it had fluctuated for a generation. The budget's expanding claim on national resources began in the 1960s with the rise in defense spending during the Vietnam War. When the defense effort wound down, the federal budget did not, as Congress and the Nixon administration collaborated to invest the "peace dividend," as well as the expected returns from economic growth, in a massive expansion of Social Security, Medicare and related benefits. Other programs also grew, but not nearly as rapidly as the social insurance entitlements with their direct link to the cost of living and their sensitivity to unemployment levels.

The low growth and high inflation of the 1970s produced an automatic surge in these entitlements and with it a sense of powerlessness within Congress to control federal spending. President Carter's attack on the budget won few supporters. Social Security, unemployment insurance and similar programs were close to untouchable. Many other expenditures were protected by powerful lobbies. Only a sharp attack on programs for the poor could supply the dollars needed to cut the budget and increase defense spending as the administration had pledged to do.

President Reagan, by supplying the missing ingredient of leadership -- as well as a stronger stomach for stern measures -- has now carried the day for the budget side of his economic program. The politics of the remaining portion, the tax proposals, will be quite different. It may be much harder to muster conservative support for a policy that will continue the federal deficit at close to its current level throughout 1982 -- a level acknowledged by the administration to be more than $60 billion, but which is thought in some other quarters to be closer to $70 billion.

Budget-cutting is not an end in itself but presumably a remedy for some substantial ills. Last summer, when his program was essentially shaped, President Reagan decided that slow growth and inflation were the main sources of economic malfunction. The economy, however, has stubbornly refused thus far to display the expected degree of weakness, rasing further questions about the wisdom of a stimulative cut in personal income taxes. The inflationary bias built into the economy and its vulnerability to price shocks from energy, food and other critical resources are not addressed by the administration's currect policy. And while there is clearly a political base for returning the budget to its traditional relationship to GNP, the job of building support for a real anti-inflation program -- and all that implies for crucial constituencies like the middle-class work force -- has not really begun.

Having won a considerable victory for its budget plan, the administration has a great deal of power to decide where to go next with its economic strategy. The real test of its competence and leadership will come, however, less in its ability to push through a strategy conceived many months ago than in its ability to show that it can deal thoughtfully and flexibly with an economy that is both changing and, to a large extent, unpredictable.