WHILE THE White House continues working through the details of its budget plan, the outlines of a consensus are beginning to emerge on Capitol Hill. Support is building in both parties and houses for a broad, temporary freeze on almost all types of federal spending -- a strategy at once fairer and more effective than the freeze-plus-cut-plus-buildup plan being floated by the administration.

The day after he was chosen as majority leader, Sen. Bob Dole endorsed the idea of an across-the- board freeze as an alternative to the administration's selective cuts. Senate Budget Committee Chairman Pete Domenici has specifically stated that Social Security -- the mere mention of which sends shivers through the White House -- must be included in any freeze. The new Senate Armed Services Committee chairman, Sen. Barry Goldwater, has bluntly informed the Pentagon that the coming Ice Age will extend into its territory as well.

There is also support among Senate Democrats. Sen. Ernest Hollings has long promoted a broad freeze. And last year, a plan built around a freeze on most programs, came within one vote of Senate passage with full Democratic support. That plan was sponsored by Sen. Lawton Chiles, who, interestingly, has decided to challenge Sen. Robert Byrd for the job of minority leader.

Over in the House, Rep. William Gray, a leading contender for Budget Committee chairman, indicated last week that he could go along with a freeze plan if it were fairly applied to all parts of the budget. Speaker Thomas P. O'Neill has offered to cooperate in restraining the non-defense budget as long as the president is also willing to restrain military spending and get out in front on unpopular changes.

A broad-based budget freeze offers considerable potential for narrowing the deficit. The one-year freeze plan sponsored by Sens. Nancy Kassebaum, Charles Grassley and Joseph Biden, would produce yearly savings of almost $80 billion by 1988. Sen. Domenici is suggesting a partial three-year freeze plan on both spending and tax indexing that, while sparing programs for the very poor, would save $110 billion by 1988 and, when interest savings are also included, reduce the 1988 deficit by almost $130 billion.

Add to Sen. Domenici's plan some needed reforms in the tax system, farm supports and other aid programs being proposed by the White House, and you would have a truly serious assault on the deficit. Of course the program would still be far from painless, and even without Speaker O'Neill's cautionary message, it is hard to imagine prompt action without strong presidential leadership. In his Friday press conference the president remained firmly opposed to any limit on Social Security. But he seemed to signal willingness to consider real restraints on defense -- not just the reestimations of overinflated costs that have passed for defense savings in previous budget cycles. Perhaps the consensus that seems to be building in Congress will encourage the president to move in the direction of further compromise.