The hard-pressed government of Poland has asked the United States for a whopping $3 billion in emergency economic aid, generating surprise and a policy dispute among officials of the outgoing Carter administration.

Administration sources on all sides of the issue said yesterday it is unlikely that the United States in this stage of governmental transition will be able to make a commitment anywhere close to the imposing sum which was requested by the Warsaw regime several weeks ago.

However, a high White House official said "incremental" U.S. aid well short of the figure requested is under active consideration and might possibly be approved.

The Polish request for a new program extending over several years caught the Carter adminstration at a time when its days in power are running out. The position of President-elect Ronald Reagan on the issue is unknown, according to adminstration officials who expressed doubt that any large-scale program is practical without approval of Reagan and probably of Congress.

Carter administration spokesman declined to comment on the record yesterday on the Polish request, which was reported by William Beecher in The Boston Globe. Speaking on a "background" basis (not for quotation by name), a State Department official told reporters at the daily departmental news briefing that the United States is considering a recent aid request from Poland.

Other sources said the Polish request calls for half or more of the multi-year program of aid to the furnished in the first year, in view of the economic straits of that Eastern European country and the potential cost of meeting the demands of the newly authorized independent trade union movement there.

Officials familiar with the proposed program said that Poland is asking primarily for concessional loans and rescheduling of payments on existing debt. While these would be more feasible for the United States to provide than outright grants, particularly in the light of the congressionally imposed ban on aid to communist countries, even loans or debt rescheduling in such large amounts would present formidable problems.

After the surprise victory of the Polish workers' movement in late August, the United States provided $670 million in Commodity Credit Corp. credit at commercial rates for food purchases. At the time, U.S. sources said yesterday, the authorities in Warsaw were told that not much more would be forthcoming in the short run.

In view okf this, Washington officials were startled at the enormous request received through the Polish Embassy here in the latter part of last month. One official speculated that it reflected a misunderstanding by the government in Warsaw of what the United States is willing and able to do at this stage.

The total debt of Poland to western nations is reported to be about $21 billion, the largest of any communist bloc nation. Of this sum, about $2.5 billion is owed to United States sources -- around two-thirds to private banks and the rest to the government.

Poland's request for $3 billion, therefore, exceeds the total amount of outstanding loans from the United States, private and public.

Secretary of State Edmund S. Muskie and White House national security affairs adviser Zbigniew Brzezinski, both of whom are of Polish ancestry, are reported to be arguing within the administration for an energetic effort to do all that can be done in present circumstances. The central argument for early action is that the United States should support the Polish government and trade unions at this critical moment in the unprecedented development of independent unionism in the communist bloc.

Officials of the Office of Management and Budget and the Treasury and Agriculture departments are reported to be skeptical about providing substantial aid at this time. Without basic reforms of the Polish economic system, these officials maintained, new aid would be quickly dissipated.

Another consideration in the U.S. discussions is the extent of efforts to be made by Western European countries that have large economic and political stakes in Poland. It was unclear last night how much new aid is being contemplated by the Western Europeans.