President Carter and Democratic leaders in Congress agreed yesterday to draft a joint tax-cut plan to take effect in 1981, but left unsettled the size and makeup of the bill and when it might be pushed to passage.

Although Carter asserted repeatedly that he wants to keep his options open, officials said the White House is making room in its revised budget estimates for a $20 billion to $30 billion cut and now expects a tax reduction in 1981.

While officials deny it, that stand would mark a retreat from the position Carter took last January and again in March when he proposed leaving tax rates intact through late 1981, in part to help balance the budget and fight inflation.

With the economy in a recession, Carter now seems prepared to accept a tax cut in early 1981 provided government spending is restrained sufficiently. But, partly as a face-saving measure, he wants tax legislation put off until after November.

Senate leaders, following their meeting with the president yesterday, appeared to be edging toward grudging acceptance of his request to delay final passage of any tax bill until after the election.

Sen. Lloyd M. Bentsen (D-Tex.), a leading tax-cut proponent, told reporters that while the Senate Democrats will honor their pledge to draft a tax-cut bill by Sept. 3, he no longer is sure such a bill could get through both houses before the November election.

Sources on both sides suggested that a likely compromise might be for the Senate to take up its bill in August and September and for the House to put off any action until a special session after the election.

House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) already has raised the possibility of a post-election session. Yesterday, he told reporters: "We're trying to do it [pass the tax-cut bill] in a nonpolitical manner."

White House officials made clear yesterday that the timing of congressional action on the tax-cut legislation is an important factor to the president. Officials say they fear that the lawmakers could run amok in a preelection rush.

Press secretary Jody Powell said Carter does not intend to disclose his tax-cut proposal this summer, in part to give the administration more leverage against an eager Congress as the election approaches.

However, Powell told reporters that the president would agree to a tax-cut bill this year if it met his specifications. "That's where we expect to go," Powell said, "toward a tax cut in '81."

Yesterday's developments followed a breakfast meeting between Carter and key congressional leaders in which the two sides set up a joint task force to hammer out details of the tax-cut legislation.

Carter used the same kind of White House-congressional negotiations to work out specifics of his March 14 anti-inflation plan. Yesterday, the House and Senate tax-writing committees agreed to start tax-cut hearings this month.

The coordinated effort represents an attempt by the White House to regain control over the tax-cut issue. Senate Democrats last week stampeded past the president and pledged themselves to provide a tax cut this year to match one proposed by GOP presidential candidate Ronald Reagan.

In a surprise last Wednesday, Reagan proposed a 10 percent across-the-board tax cut for 1981, combined with faster depreciation writeoffs for business -- essentially repackaging an early plan to preempt Carter's tax-cutting efforts.

By the end of last week, House leaders, who earlier had been against taking up tax-cut legislation this year, concluded reluctantly there was no way to hold the line once the Senate had promised a package of its own.

Carter had been trying to buy time by urging House and Senate leaders to put off any action until after the White House completes its mid-year budget and economic forecasts, now scheduled for late this month.

The White House is trying to protray the Democrats' new joint approach as a "responsible" way to draft tax-cut legislation, in contrast to what it calls Reagan's more "political" tax-cut plan.

Although Powell reiterated yesterday that the Democrats have made no decisions on their tax-cut package, sources say it almost certainly will be smaller than Reagan's $36 billion tax-cut plan and contain smaller reductions for individuals.

Enactment of a tax-cut would shatter whatever little hope is left of balancing the fiscal 1981 budget, which already is expected to be $20 billion or so in deficit because of the impact of the recession.

Officials said a tax reduction of between $20 billion and $30 billion for calendar 1981, as the administration is now considering, would add $10 billion to $15 billion to the fiscal 1981 deficit.

That means the overall red-ink figure for fiscal 1981 could run as high as $30 billion, provided the recession doesn't worsen further and spending remains intact. Fiscal 1981 ends a year from Sept. 30.

Both Bentsen and O'Neill appeared to interpret the president's remarks yesterday as a green light from the White House to go ahead with tax-cut legislation. The speaker said there now was "no question at all" there will be a tax cut in 1981.

Carter also cautioned the lawmakers yesterday that he still expects to see Congress complete its budget-cutting action before enacting a tax reduction. And he hinted that he would not support a tax-cut plan he thought would be inflationary.

Powell insisted to reporters that the administration's plan to make room for a tax cut in its new budget and economic forecasts was not not necessarily an indication that the president was committed to a 1981 tax cut.

However, he added, "That's where we expect to go . . . and this way it's a more honest presentation. It's more likely that you will have [a tax cut in 1981] than that you won't have one."