President Reagan, in his first response to heavy Republican pressure to compromise on the 1984 budget, sent his top aides to the Senate yesterday with a counter-offer to split the difference on defense and domestic spending next year while holding firm on his tax program.

But they returned without an agreement after at least two conservatives objected to Reagan's proposal for standby tax increases of about $150 billion over three years starting in 1986, according to several sources.

The split in GOP ranks apparently doomed the proposal because a budget along the lines Reagan proposed would break with the bipartisan approach followed by the Senate Budget Committee and gain few if any Democratic votes, requiring total GOP unity for passage.

Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) said afterward that "little or no progress" had been made toward reaching an accord among Republicans that would enable his stalemated committee to agree on a budget resolution. "I think it's fair to say I'm not very happy today," he added.

But he later issued a statement saying the committee will meet meet again today in hopes of reaching an agreement by Friday.

"We must continue to try to get a compromise, or the deficits will threaten economic recovery," he said.

As the Republicans were squabbling, Senate and House Democratic leaders met and issued a statement accusing the White House of showing a "cavalier attitude toward the budget process" and accusing Defense Secretary Caspar W. Weinberger of trying to get Reagan to "scuttle the process entirely."

Said the Democrats: "We urge the president to reject this advice. Failure to approve a budget resolution will send deficits and interest rates through the ceiling and abort the recovery.

"We urge the president to work with the Congress in achieving a budgetary compromise, a compromise that will put the budget under control and put Americans back to work."

According to sources at the GOP strategy session, attended by presidential counselor Edwin Meese III, chief of staff James A. Baker III and Office of Management and Budget Director David A. Stockman as well as GOP leaders and members of the Budget Committee, taxes were the key stumbling block.

In his original budget, reaffirmed in yesterday's offer from the White House, the president proposed only nominal tax increases in fiscal 1984 and 1985 but would raise taxes by an average of $50 billion a year for the following three years if deficits continued high, if the economy was still recovering and if Congress agreed to his spending cuts.

Democrats want considerably higher tax increases than Reagan has proposed, starting with up to $30 billion next year. That would imply repealing or capping the 10 percent income tax cut that is scheduled for July plus repealing inflation adjustments for tax rates thereafter.

But at least four and perhaps five of the conservative Republican members of the committee object to any tax increases, including the standby taxes for 1986 and beyond that Reagan has proposed.

"Many of us support the president on taxes, others want much more in new taxes and some want to allow the deficits to continue to rise toward $200 billion," said Domenici in what appeared to be a slap at conservatives who want no tax increases.

Reagan's split-the-difference offer on defense would mean an after-inflation increase of 7.5 percent for next year--halfway between the 10 percent that Reagan has proposed and the 5 percent that the Budget Committee approved--although Senate sources said it would give Reagan about 95 percent of what he wanted over five years. This was the formula that Majority Leader Howard H. Baker Jr. (R-Tenn.) recommended earlier this month and Reagan indicated he would approve until Weinberger objected.

On domestic spending, sources said the White House wanted the Budget Committee to cut about $6 billion of the $11 billion it had added to the president's plan, although he would have gotten three-fourths of the domestic savings he was seeking over three years.

While most members who wanted the domestic spending add-ons indicated that they would compromise if the conservatives would, at least two of the conservatives, Orrin G. Hatch (R-Utah) and William L. Armstrong (R-Colo.), were said to have refused to budge.

This left the committee without enough votes for passage of a budget because the Reagan offer would gain few if any Democratic votes and, with a 12-to-10 split in favor of Republicans on the panel, loss of even one GOP vote can lead to a tie if Democrats vote as a bloc.