Carter administration officials yesterday conceded privately that their proposed $25 billion tax cut for this year "may run into trouble" in Congress as a result of yesterday's announcement that unemployment dropped sharply at the end of 1977.

They insist that the economic case for a major tax cut is still compelling. "We didn't design the tax cut to rescue the economy, but to keep the recovery going," said Charles L. Schultze, chairman of the Council of Economic Advisers.

But the perceived rationale for a tax-cut stimulus, which Carter approved last fall when the unemployment rate seemed stuck at 7 per cent, is altered by the dramatic drop in the rate to 6.4 per cent in December. That is lower than the rate projected by most economists - including the President's - for all of 1978.

One authoritative congressional source said yesterday that the administration had always underestimated the difficulty in getting a tax cut passed this year, "and the good unemployment result will now make it a little harder," assuming that the rate doesn't flare up again.

This source pointed out that many members of congress especially on the two Budget committees, "are concerned with big deficit numbers, and a $25 billion tax cut could mean rising deficits for three years running. That's pretty hard for them to explain to voters."

If statistice over the next several weeks confirm that the economy's performance "wasn't as bad as we thought in 1977, then they'll have to base the tax-cut case on a 'growth recession' for 1979, and that's a long way off," the source said. A growth recession occurs when real economic growth, continues, but too slowly to keep unemployment from rising.

On the other hand, considerable political momentum for a tax cut still exists because 1978 is a congressional election year, and many Republicans as well as Democrats have - for varying reasons - argued for a tax cut. Former President Ford, for example, urges a hefty series of tax cuts, primarily for business as an investment stimulus.

"I didn't think the $25 billion tax cut was necessary to stimulate the economy," Republican economist Herbert Stein said in a telephone interview, "and to the extent anyone thought so, the unemployment result ought to reduce the apparent urgency."

But Stein, chairman of the economic council in the Nixon and Ford administrations added: "No one will be against a tax cut - that's like shooting Santa Claus."

Nevertheless, experts on Capitol Hill said that "it will be harder" for President Carter to get the exact tax package that he wants, and that seemingly brighter economic prospects will also strengthen the hand of those who want to keep tight control of federal spending.

A House Budget Committee staff member suggested that one result might be a tax cut of about $15 billion, effective Oct. 1, with an additional $10 billion scheduled for Jan. 1, 1980. That would not only space out the stimulative effect of the reduction, but also reduce the prospective budget deficit for fiscal 1979, which starts Oct. 1

Members of Congress dedicated to holding down government spending are expected to argue that the economy has enough momentum of its own without special jobs programs of the kind proposed by Labor Secretary Ray Marhsall. "If the tax cut is untouched, it will arm a guy like Muskie," said one observer, referring to Chairman Edmund S. Muskie (D-Maine) of the Senate Budget Committee.

Commerce Secretary Juanita M. Kreps said in an interview that "the case for the tax cut isn't weakened at all."

Don't forget," she said, "a jobless rate around 6.5 per cent is still too high. There's nothing to change our forecast that economic growth will be no more than 4.5 per cent to 5 per cent this year, and that's not enough to cut unemployment very much."

A report prepared by the Senate Budget Committee for use in the upcoming session lays out an argument for a tax cut of $30 billion. It estimates there will be a restrictive budget swing of $25 billion to $27 billion from this fiscal year to the nest. The deflationary elements include the effects of tax increases involved in Social Security and unemployment insurance legislation, the probable tax consequences of energy legislation, and extra taxes collected by the Treasury when inflation pushes individuals and businesses into higher tax brackets.

But a Senate Budget Committee official admitted "the lower unemployment number may take a little political edge off" the report's recommendation.

Democratic economist Walter W. Heller, who last week, along with Brookings Institution economist George Perry, proposed a $35 billion tax cut, agreed yesterday that the good news on the unemployment front "is bound to weaken the resolve for a strong stimulus program."