Worried by the growing "anti-bureaucrat" mood of Congress, House leaders hope to salvage a bill giving job demotion "insurance" to federal workers by linking it to President Carter's Civil Service reform plan.

Originally, Rep. Robert N.C. Nix (D-Pa.) hoped to have the House vote independently on his legislation, which is backed by the White House. The Nix bill would prevent downgradings or demotions of federal workers caught up in reorganization-related shakeups, or whose jobs were found to be overgraded through no fault of their own. (A recent Civil Service Commission study indicated that as many as 1 of every 5 federal jobs may be overgraded).

The Nix bill also would extend that downgrading protection back to Jan. 1, 1977.

That means anyone domoted since then (except for cause or because of a reduction in force) would get his or her old grade back.

White House aides-consider the Nix bill essential to make good on the president's promise that nobody in government would be hurt by his reorganization plans, and to soften bureaucratic opposition to agency reshuffling plans. During any reorganization, employes tend to get bumped around and often suffer demotions in the process. The Nix bill would prevent most of that.

Under the original timetable, the House Rules Committee would have begun hearings today on the Nix bill. That committee acts as the traffic cop of Congress, approving and scheduling bills for full floor vote.

While the votes for the Nix bill are solid in the rules committee, insiders say it could be verbally kicked to death on the House floor. Reacting to voter anger over government spending and "bureaucrats," Congress has been dealing harshly with federal employe benefit bills as elections draw near.

"In view of what has been happening to 'good' federal employe legislation up here lately," a key House staffer said, "we decided it would be best to link the Nix bill to the reform plan. That's why we asked the rules committee to let it drop. This way we will have the time, and ammunition to get it through both the House and Senate."

The strategic change seems, at this point, a wise one. Most members of Congress view the president's "reform" plan as something that will make the bureaucracy shape up. Besides, everybody likes to say they voted to reform something, especially something like the government.

Insiders expect the House Post Office-Civil Service Committee will clear the full "reform" package, with the Nix protection bill, in mid-July.