Congress finally cleared the first piece of President Carter's economic stimulus package yesterday - a $4 billion public works program to create an estimated 160,000 jobs.

Part of the $31 billion package sent up as urgent legislation in January to pick up the sluggish economy, the jobs bill was delayed nearly two months by a House-Senate dispute over water pollution policy.

Purpose of the jobs program is to create jobs quickly by making grants for local projects already planned that could be put under construction in 90 days. It took about six months to actually start a $2 billion public works program enacted last year. But the new grants will go to projects on last year's original application list and should move faster.

The House had passed the $4 billion public works bill in February. Early in March the Senate voted the same amount but added $9 billion to continue funding the unrelated program of sewage treatment plant grants designed to clean up the nation's waterways.

The House insisted that if the Senate wanted water treatment money in the jobs bill it accept policy changes opposed by environmental grups.

Environmentalists, supported in the conference by Sen. Edmund S. Muskie (D-Maine), were especially opposed to amendments that would restrict the power of Army engineers to regulate disposal of dredged and fill material in waterways, would extend deadlines for installing advance treatment facilities and would permit use of taxes rather than user fees to operate treatment plants.

Finally, in order to get the public works program started before the construction season ends, the conferees dropped both the water funds and substantive amendments and set the public works bill free. Muskie plans hearings on the water program and new legislation on it later this year.

The House gave final approval to the public works bill yesterday, 335 to 77. The Senate approved the conference report Friday, 71 to 14.

The bill also contains Senate language directing that work continue for the rest of this fiscal year, ending Sept. 30, on the dams and other water resource projects that Carter wants deleted from next year's budget as no longer worth the cost or harmful to the environment.