Poland's continuing hand-to-mouth stretch to feed its people and preserve its precarious experiment in liberalizing Communist rule has brought a new plea to the Reagan administration for $200 million in emergency U.S. food credits.

Administration officials said yesterday that the new request "will receive sympathetic consideration." They acknowledged, however, that they have not yet figured out how to satisfy the request in light of the "extremely difficult" budgetary snarl entangling the administration.

In October Poland submitted a request for $740 million worth of credits to buy agricultural products and feed grains from the United States during fiscal 1982. Because that shopping list requires prolonged consideration, Poland three weeks ago asked the United States to expedite $200 million of that sum on "an emergency basis."

Once again, as last summer, the most acute need is literally "chicken feed"--grain to sustain Poland's poultry industry, the most effective supplier of quickly produced protein. With the winter approaching, tempers are rising in the long lines outside Poland's meagerly supplied food stores.

Political observers agree that this makes Poland vulnerable to combustible interaction between food shortages, street demonstrations and the tense bargaining between the Communist Party and the leadership of Poland's Solidarity movement.

Rep. Edward J. Derwinski (R-Ill.), an activist in stimulating support for the Reagan administration's decision last summer to supply Poland with 360,000 tons of poultry feed by liberal interpretation of credit rules and legislation, expressed optimism yesterday that the White House will follow a similar course again.

The $200 million emergency credits will keep the same grain feed supply line from running out in January, while the overall request for $740 million in 1982 foodstuffs credits is being weighed.

"All my vibes are good," Derwinski said. "There are no political backfires on this one so far as Congress is concerned; it's the administration that has to untangle its own processes."

Derwinski said he plans to meet today with senior administration officials to explore formulas for expediting the aid.

So far as Secretary of State Alexander M. Haig Jr. is concerned, Derwinski said, "He fully understands the problem." Haig has said that Poland is involved in "a historically unprecedented evolution in political change," and American responses to Poland's requirements must be considered in that light.

Administration officials were wary yesterday, however, about forecasting how the White House this time may thread a path through the more-impenetrable budgetary thicket.

President Reagan has registered his interest in the Polish dilemma several times, most recently a week ago by authorizing $30 million more in dairy products from American surplus stockpiles to be distributed to Polish children, the aged and others by U.S. voluntary organizations such as CARE and Catholic Relief.

Beyond food credits or grants to Poland, the United States and other nations are groping for formulas to deal with the problem of multibillion-dollar long-term loan rescheduling to salvage the crippled Polish economy.

This is a contentious subject in the Reagan administration, which is facing heavy crossfire over its battered budgetary concepts.