A House trade subcommittee today will debate a resolution giving the president authority to negotiate and implement an agreement with the Japanese government to limit the number of small, gas-efficient Japanese cars sold here.

But how far the bill will get in the lame duck session is uncertain. An aide to House Speaker Thomas P. (Tip) O'Neill said that leading Democrats yesterday discussed the agenda for the remainder of the session "and that bill didn't even come up."

The resolution, introduced by Rep. Donald J. Albosta (D-Mich.), originally wasn't expected by many trade observers to get anywhere during this session. It gained momentum after the International Trade Commission on Nov. 10 ruled, contrary to positions of the United Auto Workers and Ford Motor Co., that the major causes of U.S. automakers' financial and employment woes were not imports from Japan. The causes, they said in a 3-to-2 decision, were the recession and high-priced gasoline, which drove consumers away from large and unaffordable cars.

Ford and the UAW had asked the ITC to recommend to the president that auto imports, particularly those From Japan, be limited or have protective tariffs placed on them.

After the ITC's decision, the UAW and Ford pinned their hopes for import relief on Congress, which could give the president authority to negotiate an agreement with the Japanese limiting foreign car sales here. However, at a House trade subcommitte hearing on Tuesday, U.S. Trade Representative Reubin Askew said President Carter would leave the matter up to President-elect Reagan, who has made no comment on the subject.

Several congressmen, including House Ways and Means Chairman Al Ullman (D-Ore.), said during the hearing that Congress may be sympathetic to Detroit's pleas and pass the resolution.