The Bush administration's new claim that the federal budget can be balanced in three years, which accompanied the weekend deficit reduction agreement, hinges on White House hopes that a recession can be averted and that soaring oil prices will turn sharply downward again next year.

In their updated projections for 1990 through 1995, Bush economists are counting on a drop in world oil prices to help the economy bounce back late next year from a period of slow growth that has already lasted for a year and a half.

The oil price assumption, in turn, is dependent upon resolution of the current confrontation with Iraq quickly enough to knock the average price of domestic crude, currently just under $40 a barrel, down to $24.15 during 1991 and to $21.10 in 1992.

White House economists do not see recession in 1991, but rather project the economy will grow at 1.3 percent next year, after allowing for inflation, picking up to 3.8 percent in 1992.

The forecast is similar to that of a number of private economists, who also assume that the situation in the Persian Gulf will be resolved one way or another -- and that if the resolution involves a war, the ability of Saudi Arabia to produce oil will not be significantly damaged -- by next spring.

But it is more optimistic than those of other private forecasters, such as Donald H. Straszheim, chief economist of Merrill Lynch & Co., who declared late last week, "We are in a recession: The U.S. economy fell into a recession around mid-year -- before the Persian Gulf crisis erupted."

"Some of the economic forecasting used to arrive at the {deficit reduction} targets may, in fact, be too optimistic," said Drew Lewis, chairman of the Business Roundtable, a lobbying organization for major corporations. "But there is no question that this is real deficit reduction, of the magnitude the roundtable for years has called for," said Lewis, chairman of Union Pacific Corp.

A recession, if it occurred, would not have much effect on the specific spending cuts and tax and fee increases included in the budget agreement. Likewise, the proposed $500 billion worth of deficit reductions over the next five years would not be dependent on how well the economy performs.

But a recession could cause the federal budget deficit to soar beyond $300 billion this year even if the proposed $40 billion deficit-reduction package for 1991 is enacted.

The new forecast already shows a track for the U.S. economy far enough below what the administration was predicting only two months ago, that adoption of the predictions raised the projected deficit for this year by $30.4 billion and those for the 1991-95 period by a total of almost $200 billion. In other words, the deficit outlook had deteriorated to the point that $200 billion worth of the proposed $500 billion in spending cuts and tax and fee increases will go just to offset the effect of the worsened economic outlook, according to the figures released by the budget negotiators.

Even with passage of $40 billion worth of deficit reduction measures for 1991, this year's gap between federal income and spending is projected to be a record $253.6 billion. That figure would not be as high, however, as some of the deficits in the mid-1980s when compared to the size of the U.S. economy.

To guard against having a further deterioration of the economic outlook cause problems next year in meeting a new target for the fiscal 1992 deficit, the budget negotiators proposed changing the way in which the Gramm-Rudman-Hollings deficit reduction law works.

If the changes are adopted, next March administration and congressional representatives will agree on an economic forecast that would be used in projecting the 1992 deficit even if the outlook changed between then and the beginning of the fiscal year. That way a decline in economic growth could not cause a large sequester -- a set of automatic spending cuts in discretionary spending programs triggered if appropriations exceed a set amount -- as nearly happened this week.

The negotiators also agreed on a set of other changes, including increasing from $10 billion to $15 billion the amount by which the Gramm-Rudman-Hollings target could be exceeded before a sequester would take effect, to lessen the impact of economic changes on the budget process.