With both the White House and leading senators warming to the notion of a budget "freeze," you get the impression that real progress is being made toward reducing the frightening federal deficit. But that surface unanimity disguises a huge gap between the president's apparent notion of what a freeze would mean and congressional views on a feasible plan.

A temporary freeze, broadly applied, could produce substantial savings without reordering spending priorities or sharply reducing any particular program. Because it asks all beneficiaries of federal largess to share a national burden, it seems fair to most people.

If federal spending could be kept at its current nominal level for a year, the deficit would automatically be lessened by about $40 billion, because revenues would grow with inflation while outlays would not. Of course, this would amount to an effective cut of 4 percent or more in the program purchasing power. But that loss should be relatively supportable for all but the very poorest beneficiaries of federal programs. And they might be exempted from the cut since their benefits constitute only a small portion of the $1 trillion the government will spend next year.

The president's idea of a freeze, however, evidently shares none of these virtues. Because huge deficits have ballooned interest on the debt, and because Mr. Reagan insists on continuing to increase annual military spending and on exempting Social Security from further cuts, his freeze would either net very little in the way of savings or would require closing down major parts of the government.

By OMB's (and everyone else's) calculation, a freeze on the roughly one-fourth of the budget that is touchable would yield less than $9 billion in savings next year. To reac the president's goal of cutting the deficit by more than $100 billion by 1988, a meat ax would have to be taken to such programs as education and training, national parks, law enforcement and the environment.

A more productive and workable version of a freeze, proposed last year by Sens. Charles Grassley, Nancy Kassebaum and Joseph Biden, would put a one-year freeze on farm target prices, cost-of-living adjustments, federal pay, hospital and doctor fees -- the works. The Pentagon could go on buying at its current much-increased level, but for one year the rapid escalation of its purchasing power would be interrupted. The plan is gaining popularity on the Hill. But gaining administration agreement would require a considerable thaw in some hard-frozen presidential views.