The Republican Senate, miffed at President Reagan's economic advisers for suggesting that budget deficits are less important than party rhetoric has traditionally made them, yesterday demanded immediate action to achieve Reagan's abandoned campaign promise of a balanced budget by 1984.

What started as routine consideration of a relatively meaningless budget resolution exploded into a political firestorm for Reagan when senators read morning newspaper accounts of remarks by the economic advisers suggesting that the evils of deficits have been exaggerated.

The White House spent much of yesterday disowning the remarks. Details on Page A9

Democrats, meanwhile, gloated over the heresy, vowing their own fealty to the "old-time religion" of balanced budgets, while Republicans squirmed in anguish both on the Senate floor and in a private leadership meeting with Reagan.

"It can't happen anywhere but 'Fantasy Island' to have large deficits and not have economic disaster," claimed Sen. William L. Armstrong (R-Colo.) in a speech warning his colleagues that condoning deficits would sound the "death knell of the Republican Party."

"What chance do we have to bring fiscal discipline . . . ," asked Budget Committee Chairman Pete V. Domenici (R-N.M.), "when we have the economic advisers to the president saying, 'Don't worry about balanced budgets' ? "

Even as the debate was warming up, Republican leaders from both houses were urging Reagan privately at a White House meeting to disavow the advisers' comments, according to aides to the leaders.

At the end of nearly six hours of debate, the Senate amended the budget resolution to call on its Budget Committee to prepare, by next March 31, a plan for balancing the budget by 1984.

This was added to earlier language urging Reagan to do the same "as soon as possible"--an appeal originally proposed by Democrats that Armstrong, in leading the charge yesterday, apparently felt needed to be strengthened.

The vote on Armstrong's proposal, which was embraced by Domenici and other Republican leaders when Armstrong could not be dissuaded from pushing ahead with it, was 50 to 47. Nearly all the dissenters were Democrats, who had earlier pushed their own balanced-budget amendment, losing on a nearly party-line vote.

Unlike the Democratic proposal, which did not specify how the deficit reductions should be accomplished, the Republicans called for "spending reductions in all parts of the budget, including entitlement programs," as well as tax increases --although they specifically ruled out a rollback of the tax cut that Congress approved last summer. Reagan has been cool to the idea of any tax increases.

The Senate finally approved the budget resolution, but only by a vote of 49 to 48, with nearly all Democrats dissenting and with even Republicans claiming it was meaningless.

In theory the resolution was supposed to set binding ceilings for the fiscal year ending next Oct. 1. But because Congress and the administration could not agree on further budget reductions, it merely rubberstamped an earlier resolution setting spending and revenue targets, leaving all major tax and spending decisions until next year. As a result, the resolution anticipates a $37.6 billion deficit, when even the administration's Office of Management and Budget now says the deficit will be $109 billion without additional spending cuts or new taxes.

"If the flag we're asked to rally around is the flag of a $100 billion deficit," said Sen. Slade Gorton (R-Wash.), "I submit there will be few rallying around that flag."