The White House has taken the unusual step of ordering congressional lobbyists from all across the government to press their House friends to support draft registration.

"We've done this kind of thing before," one administration official said yesterday, "but we save it for the big ones."

Getting Congress to go along with registering 4 million 19 and 20-year-old males, starting this year, has thus been put in the category of "must win" by President Carter. He has given up on getting Congress to authorize the registration of women.

The full-court press on House members was ordered on Monday at a meeting of administration lobbyists in the White House called by Frank B. Moore. Carter's chief liaison officer with Congress. Gary L. Fontana from the Office of Management and Budget outlined the game plan for draft registration, according to participants.

Carter's plan to issue an executive order to require men to register at their local Post Office is meaningless until he receives the money from Congress to finance it.

A House Appropriations subcommittee, on an 8-to-3 vote, last month refused to approve the $13.3 million in fiscal 1980 funds needed to start. The White House is trying to persuade the 54-member Appropriations Committee to reverse that decision.

Besides the political opposition, registration has bumped into the fiscal 1980 funding ceiling Congress imposed on itself. So Chairman Jamie L. Whitten (D-Miss.) of the Appropriations Committee is contemplating a resolution to tranfer the $13.3 million from the Pentagon to Selective Service to stay under the ceiling.

A coalition of national organizations is mobilizing to stop that resolution and any other measure that would finance draft registration. Antidraft leaders are organizing a demonstration in Washington for March 22.

Patrick Lacefield, a coordinator of National Mobilization Against the Draft, said yesterday that antidraft demonstrations will take place in Carter campaign offices all across the nation between now and the March 22 Washington rally.

Carter's draft registration plan ran into skepticism on Monday when a Senate Appropriations subcommittee took its first look at it. Chairman William Proxmire (D-Wis.) told administration witnesses that he is not convenced peacetime registration is needed.

Sen. Mark O. Hatfield (R.-Ore.) has said he will organize a filibuster to try to stop any bill to finance registration.

The Senate is expected to hold back on any further action on the registration money bill until after the House acts.