Senate Majority Leader Robert J. Dole (R-Kan.) postponed Senate action on the fiscal 1987 budget yesterday in hopes of avoiding a clash with the Reagan administration, but White House officials continued to resist a compromise over critical tax and defense issues.

Even as Dole was asking the White House for high-level consultations on the budget dispute, the president's budget director was saying "we're not ready to compromise" and a senior presidential aide indicated that months may pass before serious efforts at an accommodation are made.

At issue is a fiscal 1987 budget plan approved Wednesday by the Senate Budget Committee that would cut $25 billion from Reagan's defense request, raise taxes by $18.7 billion and approve only about half of his proposed domestic spending cutbacks. It was drafted jointly by Republicans and Democrats and approved by a bipartisan majority, 13 to 9.

With the Republican-controlled committee on a collision course with the White House over the budget proposal, Dole appeared to be buying time before having to take the embarrassing intraparty scrap to the Senate floor.

Budget Committee members rushed through the plan in order to get it to the floor for action before the Senate's Easter recess begins next Thursday. But Dole, citing a desire to consult with the White House, his own misgivings about the budget and pressures of other business, including a vote on aid to Nicaraguan rebels, postponed the issue until after Congress returns April 7, according to aides.

"He's in one hell of a pickle," said one colleague, speaking of the conflicting White House and Senate pressures and Dole's ambitions for the Republican presidential nomination in 1988. Playing for time "lets Dole do what he does best, which is to gather up all the strings and tie them together," another senator said.

But the message from the White House was that time was probably all that Dole would get from the administration. Rather than negotiate over budget targets, as White House officials did in the past, they have decided to lie low until appropriations battles later in the year, the senior aide said.

If appropriations bills are stalled because the budget dispute remains unresolved, this could bring the White House and Congress to an explosive showdown in September when an omnibus "continuing resolution" would be needed to fund the government in the absence of regular appropriations bills.

It could also trigger spending cuts mandated by the new Gramm-Rudman-Hollings budget control law if Congress and the White House have not achieved the $144 billion deficit target for fiscal 1987. Without spending cuts or tax increases comparable to those in the Budget Committee's plan, it now appears that the target will be missed by about $40 billion.

Some lawmakers believe such a scenario would give the White House leverage to get what it wants. Others contend that defense spending cutbacks under Gramm-Rudman-Hollings would be intolerable for the administration, thereby giving Congress important leverage of its own.

In the meantime, White House strategy calls for Reagan to withhold response to specific congressional budget votes, including ones that violate his priorities, although he will continue to oppose tax increases, argue for defense spending increases and address the broader goals of his administration.

It also calls for Office of Management and Budget Director James C. Miller III to stay in contact with Congress but not to negotiate, a strategy he reflected in an interview on NBC's "Today" show.

"We're not ready to negotiate . . . . The president doesn't want a tax increase or a cut in military preparedness," Miller said. "I think we will discuss, and discussions are going on right now. The leadership in the Senate will be orchestrating some discussions about these matters. But we're not ready to compromise away the president's principles."

Miller, however, showed some concern that Congress could force a tax increase or severe defense spending cutback on Reagan. Asked why people should care whether there is a budget, he said, "I think they should be concerned that there's some possibility Congress will force a tax increase on the president, or force a reduction in defense spending that might weaken our national defense . . . ."