In a speech framed as a positive response to President Carter's criticism, the president-elect of the American Bar Association last night asked Carter to support a federal program that would help provide lawyers for criminal defendants in state and local courts if they can't afford to hire their own attorneys.

The proposal for a National Center for Defense Services, which would cost an estimated $70 million the first year and go up to $250 million in succeeding years, is under study by the White House.

"The ball is now in the president's court," ABA president-elect S. Shepherd Tate said in a speech to the D.C. Bar Association's annual meeting.

President Carter last month accused the nation's lawyers of failing to meet their responsibilities to the public.

"I believe that the Carter administration and the ABA can work together for the establishment of the Center for Defense Services," said Tate, a Memphis attorney who takes over as ABA president in August.

Tate said many defendants in criminal cases are inadequately represented "simply because they are poor" even through the U.S. Supreme Court ruled in 1973 that anyone who faces a possible jail term has the right to an attorney.

"The resources devoted to the provision of counsel are so grossly inadequate that, frequently, overburdened, underpaid and inadequately trained lawyers provide little more than token representation," he said.

State and local governments spent $236 million for public defender services in 1976 and the Center for Defense Services would supplement that with additional money. The money would be used to hire investigators and social workers as well as for attorneys' fees.

The federal government pays the cost of attorneys for people charged in federal cases who can't afford to pay for their own attorneys. The courts in the District of Columbia are included in that federal program.

About three-fourths of the nation's criminal defendants are too poor to afford their own attorneys, said Laurence A. Benner of the National Legal Aid and Defender Association, which worked with the ABA on the proposal. Attorney's fees for someone charged with a serious crime can amount to $1,000 or more.

The National Center for Defense Services would be a parallel organization to the federally funded National Legal Services Corp., which sets up programs to supply attorneys to handle civil cases - divorces, landlord-tenant disputes and credit problems - for the poor.

Top White House aides - including counsel Robert Lipshutz and domestic policy adviser Stuart Eizenstat - asked ABA officials at a May 10 meeting why the National Legal Services Corp. could not be expanded to handle criminal cases.

Tate said that possibility had been discarded by the ABA and by experts from the National Legal Aid and Defender Association on the grounds that the two areas of law are so different that they require separate agencies.

Moreover, other sources said, the National Legal Services Corp. feared its civil programs would be swallowed up by the need, backed by court decisions, to provide lawyers for defendants in criminal cases.