The Senate began work yesterday on a revised version of the Humphrey-Hawkins "full employment" bill, with promises by two key committee chairmen to push the measure through quickly as a memorial to the late Sen. Hubert H. Humphrey (D-Minn.).

In an opening day of hearings, a joint session of the Senate Banking and Human Resources committees heard leaders of the Full Employment Action Council - the coalition of liberal groups backing the measure - call for immediate passage.

Sens. William Proxmire (D-Wis.) and Harrison Williams (D-N.J.), chairmen of the respective panels, endorsed the controversial legislation and pledged to work quickly to send the bill to the Senate floor.

The legislation endorsed belatedly by President Carter after months of negotiations aimed at softening the earlier version, already is under consideration in the House Education and Labor Committee. House leaders hope to send the bill to the floor by March 1.

As expected yesterday's hearing was filled with endorsements of the legislation and tributes to Sen. Humphrey, who was one of its two major sponsors. The other is Rep. Augustus F. Hawkins (D-Calif.), who is managing the bill in the House.

Coretta Scott King, widow of the slain civil rights leader and co-chairman of the coalition supporting the bill, said the legislation would be "as far reaching as the 1964 Civil Rights Act" and mark "a major milestone" in fulfilling her husband's dream.

The only criticism to be voiced yesterday came, ironically, from Proxmire, whos aid he thought the bill ought to have tougher anti-inflation goals - possibly aimed at reducing price rises to 3 percent by 1980. The banking committee chairman is expected to add this to the bill.

One surprise was an apparent softening of opposition by Sen. Orrin G. Hatch (R-Utah), a member of the Human Resources Committee. Hatch told the hearing he had vigorously opposed the earlier version of the bill, but thought the new format had "some beneficial provisions.

Witnesses yesterday included urray H. Finley, president of the Amalgamated Clothing and Textile Workers Union and co-chairman of the Full Employment Action Council. Finley said the measure was needed to spur the government into acting to resolve the unemployment problem.

The bill would commit the government symbolically to reducing the jobless rate to 4 per cent by 1938 and would require the president to shape his economic policies to meet their goal. Many economists contend the goal can't be met without exacerbating inflation.