The Reagan administration has sharply scaled back its controversial forecast of how much good will be done to the economy by the tax and spending cuts the president will propose next week, administration sources said yesterday.

The latest forecasts, on which the president will base his proposals, show much lower growth and higher inflation than the extremely optimistic earlier projections. Those were based mainly on the work of "supply-siders" Lawrence Kudlow and John Rutledge.

It will be far harder to balance the budget by 1983, as the administration has said it intends to do, if the new numbers are right. They show real growth in the economy of 4 percent next year, rather than the 7 percent predicted by the supply-siders. The Carter administration last month forecast 3 1/2 percent real growth for 1982 on the basis of its budget proposals. Reagan is thus now saying he cannot do much better.

Similarly, inflation next year is now forecast at about 7 percent to 8 percent. That is more than the 6 1/2 percent projection made by Kudlow and Rutledge, but still is less than the Carter forecast of a little over 9 percent on the same basis. For later years the administration is now forecasting real growth of 5 percent in 1983, followed by about 4 1/2 percent in 1984, and inflation of just over 6 percent in 1983 and about 5 1/2 percent in 1984.

Unemployment is expected to rise to 8 percent this year, and then fall back next year to a little below its present 7.4 percent rate. There may be one three-month period of negative growth this year, the sources said.

The shift in the forecasts will make them easier to defend, but at the same time will show a far smaller payoff from the Reagan prescription for the economy. This may make it harder to sell budget cuts which call for painful sacrifices now in order to reap benefits later.

The changes probably result from skepticism within the administration about the "supply-side" model. Treasury Secretary Donald T. Regan commented this week that he sometimes feels like a referee in Treasury meetings between firm monetarist Beryl Sprinkel, undersecretary for monetary affairs, and supply-sider Norman Ture, the undersecretary for tax policy. True believes that cutting taxes will spur economic growth sharply, raising more revenues through the additional growth than are lost because of the tax cut.

A conventional monetarist model of the kind used by Sprinkel before he came to the Treasury would not show the dramatic reduction in inflation and stimulus to growth that the supply-siders believe in. The Rutledge model assumes that inflationary expectations are a key factor in determining the rate of inflation, and that they are influenced sharply by spending and tax cuts.

Among these disputing the very optimistic forecasts, sources said, were Murray Weidenbaum, chairman of the Council of Economic Advisers, and Alan Greenspan, former CEA chairman under President Ford and now an outside adviser to the administration.

Earlier this week presidential counsellor Edwin Meese told a private meeting of trade association executives that the administration recognized the danger that tax cuts could worsen inflation unless spending is also cut. He said it was "not willing to take the chance" of relying solely on supply-side theory "even though we don't disagree with that as a possibility."

The administration's aim of balancing the budget by fiscal 1983 will be much more difficult if growth is slow and inflation high before then. The original optimistic estimates showed spending lower by $45 billion in 1983 just through the effect on outlays of less unemployment, lower prices and therefore smaller entitlements.

Budget Director David Stockman, when asked this week whether the administration still hoped to balance the budget by fiscal 1983, said "somewhere in that range."