Senate Democrats nervously voted down Ronald Reagan's tax-cut proposal yesterday, but only after hurriedly abandoning their balanced-budget plans and promising their own tax-cut legislation within 10 weeks.

In a reversal that caught both the House and the Carter administration by surprise, a hastily called caucus of Senate Democrats formally asked the Finance Committee to draft legislation by Sept. 3 for a major tax cut in 1981 that would compete with the Reagan plan.

A few hours later, the full Senate defeated the first of several expected GOP efforts to tack Reagan's plan onto other pending bills. The partyline 58-to-35 vote kept the tax cut off a bill lifting the federal debt ceiling.

The embarrassed Democrats were put on the defensive by Reagan's surprise proposal Wednesday for a 10 percent across-the-board tax cut for 1981, combined with faster depreciation writeoffs for business investment.

Majority Leader Robert C. Byrd (W.Va.) led the Democrats in their response, branding the Reagan approach a "Simple Simon, Tinkertoy" economic plan that would amount to writing tax policy on the Senate floor without hearings. He predicted the Democratic alternative would eventually pass.

However, GOP senators remained undaunted.Sen. John C. Danforth (Mo.) magnanimously invited Democrats to join in supporting the Reagan plan, declaring that "the consensus for a tax cut is here now."

Reagan, obviously relishing the effect his proposal has had, issued a statement saying, "Yesterday I urged the Congress to enact an immediate tax cut . . . to come to grips with the country's desperate economic decline. Today, the Democrats in the Senate answered. Their pitiful response: 'We need a study, a task force.'

"What are they waiting for?" he chided. "And where have they been all these months? What do these Democratic leaders in the Senate expect to learn . . . that millions of American families don't already know?"

The flip-flop by the Senate Democrats stunned both the White House and the House Democratic leadership. Carter's key advisers are discussing a tax-cut proposal of their own, but the president has not decided whether or when to propose it.

Carter's top four economic advisers, led by Treasury Secretary G. William Miller, met to commiserate with House Democratic leaders and key members of its Ways and Means Committee. But they cautioned that any decision on a tax cut would have to await the president's return from the Venice summit.

The action by the Senate Democrats shattered previous plans by congressional leaders to put off consideration of a tax bill during this election year. Until a few days ago, the Democrats had seemed intent on balancing the budget instead.

Reagan's thrust on Wednesday changed all that, at least for the Senate. Its Finance Committee is not committed to drafting a major tax-cut bill that includes rate cuts for individuals and investment incentives for business.

In the House, Ways and Means Chairman Al Ullmann (D-Ore.) reiterated his own opposition to a tax-cut bill this year, but conceded he may have to "rethink" that stand in view of the Senate caucus action.

At the same time, key Democratic sources reported "some slippage" in the number of Ways and Means members who oppose taking up a tax-cut bill this year.

The Democratic position on the Reagan plan is that it would be "irresponsible to consider tax legislation this year without formal hearings on the proposal in the Finance and Ways and Means committees.

Finance Committee Chairman Russell B. Long (D-La.) told the Senate in floor debate his panel would go along with the caucus demand. But, he said, "We really don't have to charge out ill-prepared" to pass a bill. Long also reminded the Senate it was still supposedly trying to balance the fiscal 1981 budget to combat inflation. He said Americans want a tax cut but "not . . . so bad that they would have it and risk more inflation."

Reagan's proposal on Wednesday was designed to preempt Carter on the tax cut issue and free himself of charges by Democrats that his previous tax proposal -- for a 30 percent tax cut over three years -- was inflationary and "irresponsible."

Yesterday's vote on the Reagan plan was almost entirely along party lines. The only exception was Sen. Lowell P. Weicker Jr. (R-Conn.), who voted against the Reagan proposal. Sen. Harry F. Byrd (Ind.-Va.) also voted against it.

The caucus yesterday appointed a 21-member task force to hammer out recommendations for a Democratic tax cut package. The group is headed by Sen. Lloyd Bentsen (Tex.), a champion of faster depreciation write-offs for business investment.

Reagan's proposal calls for a total of $35.8 billion in tax cuts during calendar 1981 and would add $22.3 billion to the fiscal 1981 budget deficit. Of the $35.8 billion total, $31.8 billion would go to individuals and the rest for faster business write-offs.

Shortly after the balloting on the tax cut, the Senate also voted down a companion proposal by Sen. William Armstrong (R-Colo.) that would have "indexed" the federal income tax system to provide automatic adjustments to offset the impact of inflation in pushing taxpayers into higher brackets.

The Armstrong amendment, rejected 54 to 39, would have carried out Reagan's earlier pledge to go ahead with the second and third years of a three-year tax cut, which was based on a bill drafted by Sen. William V. Roth (R-Del.) and Rep. Jack Kemp (R-N.Y.).