Now that the million-dollar-a-week lobbying campaign has fizzled in the Democratic-controlled House, federal and postal union leaders are looking to the Republican-dominated Senate to protect civil servants from Social Security.

The House last week approved a Social Security bail-out bill. It did so in spite of an unprecedented lobbying effort from federal and retiree groups, and costly round-the-clock radio and TV commercials that warned that the vote would be costly to the Social Security program and wreck the Civil Service retirement plan.

Union leaders lobbied hardest with friendly Democratic members and called in IOUs for past campaign favors. Despite it all, the House voted a bill to save Social Security that would put federal workers hired after January 1984 under Social Security and the CS retirement program.

Under the plan, which has White House support, present federal workers would remain in their own retirement system, which is outside of Social Security. New employes, however, would have to join and put 7 percent of their gross salary into the Civil Service pension program and 6.7 percent of their pay (on amounts up to $37,500) into the Social Security fund.

On Tuesday the Senate takes up a Social Security financing measure similar to the one already cleared by the House.

Federal and postal union leaders--some of whose jobs are riding on the outcome--hope to find a friendly senator to introduce an amendment that would delay mandatory Social Security coverage until 1985 or until a modified Civil Service retirement program could be set up for employes who would be covered by both systems.

If the Senate approved such a delay it would be one of the items to be resolved in a Senate-House conference on the final shape of the entire Social Security package.

Union leaders feel, probably correctly, that if they can get a delay in mandatory Social Security coverage for federal workers, they can get next year's election-year Congress to kill mandatory coverage. House Democratic leaders had the same feeling, which is why they pushed for the Jan. 1, 1984, coverage date for new federal workers. Most members of Congress do not want to have to deal with any Social Security issue in an election year.