The White House is expected to give the busy House Rules Committee a diplomatic nudge, and ask it to set a date for hearings on the president's no-fault demotion bill.

That legislation, included in a down-grading protection bill by Rep. Robert N. C. Nix (D-Pa.), would give pay and grade protection to workers whose jobs were slated for demotion either because of a reorganization, or through discovery that it had been improperly overgraded.

Thousands of government employes face no-fault demotions either because of erroneous classifications, or because upcoming reorganizations will force major job changes. It has been estimated that up to 30 percent of the jobs in some agencies are overgraded and therefore are ripe for pay and grade cutting.

The Nix-Carter bill would prevent downgradings and demotions (except for cause) in most cases, and restore grades to workers who have been hit by no-fault demotions since January 1977.

Last year President Carter promised federal workers that "nobody" would be demoted, take a pay cut or lose a job because of any reorganization initiated by his administration. Despite that pledge, Defense and the CIA did authorize layoffs and demotions. But most federal agencies have put the actions on "hold" becase of the President's promise.

Time is running out on some of the downgrading moritoriums granted agencies and now White House aides are anxious to get the legislation moving through Congress before reelection activity blots out everything else.