President-elect Ronald Reagan yesterday said it would be "just fine" with him if Congress passed a tax cut in the lame-duck session scheduled to start next week, instead of waiting for him to take office.

Sen. Bob Dole (R-Kan.), chairman-to-be of the Senate Finance Committee, promptly said he would press for passage of a $39 billion tax cut as soon as Congress reconvenes.

Dole said at a news conference that he had the support not only of Senate Minority Leader Howard H. Baker Jr. (R-Tenn.), but also of Majority Leader Robert C. Byrd (D.W.Va.) and of the outgoing Finance Committee Chairman, Russell B. Long (D.-La.). But House Democrats and the Carter administration, apparently caught by surprise, indicated they might continue to oppose such action.

Rep. Guy Vander Jagt (R-Mich.), chairman of the National Republican Congressional Committee and a candidate for House minority leader, said that he doubted "very, very much that many members would have the heart" to get into a protracted tax debate during the lame-duck session. He also said he doubted that the Democratic leadership would favor action on a tax cut at this time.

The Finance Committee proposal differs from the 10-percent-a-year across-the-board Kemp-Roth income tax cut that Reagan supported in his campaign. Reagan economic adviser Alan Greenspan said yesterday, however, that the two alternatives are very close in "spirit."

Both proposals would apply to 1981 taxes, those payable on income earned next year. Neither would be large enough to offset scheduled increases in the Social Security tax plus income tax increases brought on automatically each year by inflation.

In other economic developments yesterday, Reagan aides said he will move quickly after his inauguration to achieve a 2 percent "across-the-board" cut in federal spending for the 1981 fiscal year that began last Oct. 1. On some past occasions, Reagan aides have indicated he might exempt the Defense Department, whose budget he has pledged to increase, from such a spending cut, and perhaps some other programs as well. Reagan's aides did not elaborate on this yesterday.

Reagan also will impose a freeze on federal hiring, and will consider lifting the grain embargo imposed on the Soviet Union by President Carter after the invasion of Afghanistan, according to his domestic adviser, Martin Anderson.

On the tax bill, a source close to the House leadership said Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) would be reluctant to bring up a bill unless it had gone through the Ways and Means Committee. Ways and Means Chairman Al Ullman (D-Ore.), who was defeated for reelection, said through an aide that he would not speak out one way or the other until he could take up the matter with the committee members and the Democratic leadership.

The White House also said it would want to discuss the matter with the Democratic leadership before taking a stand. Dole said that a presidential veto, or the addition to the bill of "Christmas tree" amendments, could stall its passage this year.

He agreed that the Senate Finance tax measure was not precisely the bill supported by Reagan. But he denied that voters would be "shortchanged" if Congress passed the committee's bill. "The economy needs this legislation now," he said.

Dole acknowledged that one reason for going ahead with the committee's bill was that the full Kemp-Roth bill could be inflationary. It proposes a 10 percent cut in personal tax rates each year for the next three years."I'm not certain that we can do 10-10-10 without fueling inflation," Dole said.

The tax bill now before the Senate would give a tax break of $213 next year to an average middle-income family. The 10 percent rate cut previously backed by Reagan would have cut the same family's personal taxes by $315. In addition to the regular income tax cut, the Senate bill includes a proposed cut in capital gains taxes, which would mainly benefit the better-off. p

Of the $39 million total in the Senate bill, $22 billion would go to individuals and $17 billion for "productivity-linked" cuts. The latter includes some tax cuts for individuals, aimed at boosting savings, as well as cuts in business taxation.

Reagan endorsed the committee's proposals for simpler and more generous depreciation allowances for business during the campaign, switching from his earlier support for the more drastic 10-5-3 depreciation plan.

A majority of his economic advisers interviewed just after the election supported a 10 percent across-the-board cut in personal tax rates next year, possibly coupled with a commitment to make further cuts in later years, rather than pass a bill in the lame-duck session.

Dole remarked that "some of them changed their minds since then" and added that they would "have to deal with us now, too." He said he had not been able to speak to Reagan about the tax issue since Tuesday.

Dole said he supports indexing of tax brackets, so that the brackets will rise automatically with inflation. If that part of the Kemp-Roth measure were proposed, he would back it, he told reporters.

On the oil-profits tax, criticized by Reagan in the campaign, Dole said, "I hope there will be some modification," particularly to relieve those who get only small royalties from their oil. But he would not go further than that.

Dole said he saw no reason Congress should not sit into December, saying it was imperative that Congress pass a bill so that taxes could be cut from the beginning of next year, rather than waiting several months for the new administration to prepare its own bill.

The chairman-to-be joked about his nervousness and said that the Republicans in Congress did not know how to be committee chairman. He spoke warmly of Long, and said he had told the outgoing chairman that he would make him "honorary chiarman without any authority."

On the spending issue, Reagan aides are determined to cut $13 billion or more from the budget for the fiscal year that began last month, but have not disclosed what strategy they will attempt.