A House Republican leader warned Republican governors today that domestic programs will be squeezed for the next two years because there is no realistic way to achieve major savings in the defense budget.

Rep. Richard Cheney (R-Wyo.), the chairman of the House Republican Policy Committee, told a meeting of the Republican Governors Association that "there is a growing sentiment to cut" the defense budget, but that it cannot be done safely.

Those who find reason for relaxation in the succession of Yuri V. Andropov to the Soviet leadership, Cheney said, are deluding themselves.

"He speaks English and he likes Scotch, but he is not a card-carrying member of the ACLU American Civil Liberties Union ," Cheney remarked.

Cheney was one of two Washington visitors the governors heard on the final day of their post-election meeting. Secretary of Transportation Drew Lewis outlined the proposal for an additional 5-cent-a-gallon gasoline tax pending before the president, and said the highway, bridge and mass transit work it would finance from its $5.5 billion annual revenues would provide 170,000 direct jobs and an additional 150,000 "induced" jobs.

Responding to questions, Lewis ruled out any use of the money for transit operating costs and implied the president would veto a bill that opened the door to the fare box subsidies.

He said states would be given great flexibility in the use of about $2.2 billion of the new money and said the administration would prefer to distribute the funds by existing highway-aid formulas.

Cheney, speaking for the House GOP leadership, called Lewis' proposal the "only" realistic jobs program likely to come before the lame-duck session of Congress.

In other business, the GOP governors selected Illinois Gov. James R. Thompson over Missouri Gov. Christopher S. Bond to become chairman of the National Governors Association in August, 1983.

The nomination is tantamount to election at the National Governors Conference next year. Democratic and Republican governors alternate the national chairmanship; it is now held by Democratic Gov. Scott M. Matheson of Utah.