Senate Republican leaders predicted yesterday that Congress will retain key elements of President Reagan's tax cut program, including the 10 percent income tax cut scheduled for July, despite what appeared to be almost total disarray in GOP ranks over a budget for the next fiscal year.

"Boy, they're all over the place," said Sen. Mark Andrews (R-N.D.) after a caucus in which Republicans reportedly agreed on nothing except appointment of a nine-member committee to try to find some grounds for budget agreement within the Senate's Republican majority.

In the absence of such an agreement, several senators said they would not be surprised if the Senate generally goes along with a plan that was approved last week by the Senate Budget Committee with more support from Democrats than Republicans, who were prevented by internal splits from approving a budget of their own.

The committee's budget, scheduled to come to the floor Monday, would cut Reagan's military buildup by half, rejects many of his proposals for new domestic spending cuts and calls for $30 billion in new taxes next year, enough to jeopardize Reagan's tax cuts.

Sen. Dan Quayle (R-Ind.), a Budget Committee member, speculated that the Senate might go along with the spending proposals but sharply reduce the tax increases proposed for the next five years, including slimming next year's increase to roughly $9 billion.

Both Majority Leader Howard H. Baker Jr. (R-Tenn.) and Budget Committee Chairman Pete V. Domenici (R-N.M.) predicted that, regardless of the budget outcome, Congress will not repeal the July tax cut or indexing of tax rates to inflation in future years.

Nor, said Baker, is it likely to approve other major tax increases for the next two years, although both Baker and Domenici have indicated support for possible tax increases in future years, as Reagan has recommended.

It was opposition to any tax increases from Republican conservatives that led to the stalemate among Republicans on the Budget Committee. The conservatives, led by Sen. Orrin G. Hatch (R-Utah), are now pushing an alternative budget that would hold the line on taxes while reducing deficits by cutting more deeply into spending.

"Why are we raising taxes?" asked Hatch in a Senate floor speech linking the Budget Committee's plan to the budget passed earlier by the Democratic-controlled House.

"Because Tip O'Neill House Speaker Thomas P. O'Neill Jr. and the House Democrats, and now a majority of the Senate Budget Committee, tell us we must raise taxes in order to reduce deficits," answered Hatch, who describes as "nonsense" the contention that Reagan's tax cuts have caused soaring deficits.