Senate Republican leaders decided yesterday to write their own 1986 budget, include in it cutbacks in defense and probably Social Security, and finish it four days before President Reagan is scheduled to send his budget to Congress on Feb. 4.

They said their target will be deficits of less than $100 billion by 1988 and a balanced budget by 1990.

Reagan has resisted cuts in both Social Security and his defense buildup, which is one reason the White House has been unable to meet its own 1988 deficit target of $100 billion or its more immediate goal of $42 billion in spending cuts next year.

Compounding the problem, the White House yesterday backed off several earlier spending-cut decisions dealing with veterans' benefits, Medicaid and welfare for the aged, blind and disabled.

Indications of trouble for Reagan's fiscal 1986 budget also came from Democrats as Rep. William H. Gray III (D-Pa.), newly elected chairman of the House Budget Committee, said the president's plan appeared "DOA -- dead on arrival" and gave a qualified nod to the Republicans' proposal for a budget freeze.

The Senate Republicans indicated that they would retain many specific Reagan proposals to streamline, cut and eliminate programs and add them to the general spending freeze that is expected to form the basis of their budget. After a three-hour meeting of White House officials and more than two dozen senior Senate Republicans at Blair House, Majority Leader Robert J. Dole (R-Kan.) said the senators were not trying to take over the writing of the budget but rather to improve on the president's plan.

"We'd like to do a little better," he said.

Dole and several others also raised the possibility of tax increases, although they continued to insist that they want spending cuts nailed down first and to avoid raising taxes if at all possible.

"Until we see what we can do, we don't foreclose anything," said Dole, although he and others said there was little enthusiasm for tax increases among Senate Republicans.

Senate Finance Committee Chairman Bob Packwood (R-Ore.) said he thought the goal of $100 billion deficits could be achieved over the next three years with "minimal or no tax increases." But Sen. Ted Stevens (R-Alaska) said he thought that "ultimately we'll have to deal with some increases in revenues," although probably not this year.

Along with defense and Social Security cuts, Reagan has opposed tax increases.

On those three subjects in yesterday's meeting, the White House officials, including White House Chief of Staff James A. Baker III, Office of Management and Budget Director David A. Stockman, and presidential aide Richard G. Darman, gave no ground, although several senators said they believed Reagan would go along with what they will propose on defense and Social Security.

"The clear line of opposition was on revenues," said Stevens.

In briefing reporters after the Blair House session, Dole said an executive group composed of Senate Republican leaders and committee chairmen will begin meeting Wednesday to put together their budget plan, with a target date of Feb. 1.

He said the senators would then go back to the administration for further talks and hoped to schedule a Senate vote on the plan by "no later than May."

Asked whether the Senate plan would be completed before the president's own budget, Packwood laughed and said, "It'll be a close race."

In one way or another, Senate Republicans have written their own version of Reagan's budget for the past several years, although never quite so early and emphatically. Several senators indicated yesterday that White House aides, after conceding that Reagan's budget would not meet the established deficit-reduction target, seemed to welcome Senate help in filling the gap.

Although the White House fell short of its target, Sen. William L. Armstrong (R-Colo.) said the senators believed they had "a good chance to put together a package . . . that has a good chance of being enacted."

Armstrong and others said the plan will include more defense spending cuts than have been approved by Reagan and Defense Secretary Caspar W. Weinberger.

If other programs are cut, "we will see defense expenditures are reduced accordingly," said Stevens, who is chairman of the defense appropriations subcommittee.

Several also said they anticipated the Senate plan would include curtailment of cost-of-living increases for Social Security and other middle-income benefit programs, possibly in the framework of a one-year freeze. "I think it is clear we'll have to face up to that," said Sen. John C. Danforth (R-Mo.), a member of the Finance Committee, which has jurisdiction over Social Security.

In addition, Armstrong, who is head of the Senate Republicans' policy committee and second-ranking GOP member of the Budget Committee, said there was "a lot of support" for specific program cuts recommended by Reagan. "Even some people who never voted for any cuts want to go for the whole thing," said Armstrong.

But, even as the senators were endorsing many of the cuts, administration sources said Reagan was modifying some of them.

They said that, after an appeal by Health and Human Services Secretary Margaret M. Heckler, Reagan had decided to abandon an OMB proposal to eliminate next year's automatic cost-of-living increase for 4 million needy people receiving welfare payments under the Supplemental Security Income program for the aged, blind and disabled.

At the same time, Reagan reportedly also decided to drop an OMB proposal to eliminate cost-of-living increases for veterans receiving service-connected disability benefits or pensions.

According to other sources, the White House also decided to impose a less stringent cap on the growth of Medicaid outlays than the OMB had previously proposed, allowing the program to grow at the same pace as the medical component of the Consumer Price Index instead of merely at the inflation rate as measured by the so-called GNP deflator.

Heckler declined to discuss any of the White House actions, except to say through a press aide that she "is pleased with the outcome of the meeting" with the president and that any details on what happened must come from the White House.

The president's reported decision against freezing either the SSI or veterans' COLAs wiped out close to $3 billion in savings over the next three years that would have occurred had the original OMB COLA freeze plan for these programs remained in effect.

The reported easing of the Medicaid "cap" means the program would only be cut by about $5.6 billion over the next three years from levels it would have reached without a cap, instead of the $7.2 billion three-year reduction previously projected by the OMB.

At a news conference after his election by acclamation as Budget Committee chairman, Gray opposed but did not close the door on curtailing of inflation adjustments for Social Security.

He said sufficient spending cuts could be achieved without touching Social Security, adding, "I'm hoping we are going to be able to do that, but at this time I'm not able to say we are going to be able to do that."

Gray, a four-term black lawmaker from Philadelphia, went out of his way to assure more conservative colleagues that he would be a "consensus chairman."