THE REAGAN budget has now sailed through its first serious test in the Senate without a dent. The Senate has, in fact, voted a somewhat larger reduction than the president proposed. That's owed to the senators' questionable -- and perhaps reversible -- decision to try to finance the multi-billion-dollar Strategic Petroleum Reserve privately. The Senate votes indicate that the crusade to cut the budget has been, if anything, gaining momentum.

Most of the Senate Democrats, grinding their teeth, voted for the Reagan budget. They evidently concluded that there was little point in mounting a foredoomed opposition to it. They are waiting to see what happens next.

But in the House, because they are in the majority, the Democrats are in a much less comfortable and more interesting position. They can't merely duck as the Reagan budget rolls through. The central figure in this next stage is evidently going to be Rep. James Jones of Oklahoma who, as chairman of the Budget Committee, will present his own recommendations on Monday morning.

This exercise is an exquisite challenge to political judgment. The cuts must run deep enough to demonstrate a sincere devotion to thrift, and to protect the Democrats from the charge of obstructing the president. But they also have to demonstrate a greater concern for the social programs, to hold the party together. The cuts will have to be sufficiently ingenious to make Republican senators stop and think. They must be sufficiently plausible to force the White House to deal with them seriously.

At his press conference on Friday, Mr. Jones offered a few hints. He is thinking in terms of cuts that would be exceedingly large by any past standard, but not quite so large as the president requrested. He proposes to find some $4 billion next year through tighter administration -- chiefly the collection of unpaid debts to the government, and the pursuit of past audit reports that the federal agencies have ignored. Perhaps $4 billion is a little more than you can realistically expect to raise in a year from administrative improvement, but Mr. Jones is making a very useful point. To the extent that any significant amount of money can be raised from, say, better debt and tax collection, that much money will not have to be cut from social benefits. Mr. Jones is offering the thought that reducing the social programs ought to be a last resort rather than, as the Reagan administration has sometimes seemed to suggest in its zest for the job, the first resort.

Everyone at the Capitol can see that budget-cutting is extremely popular today. But congressmen of both parties are anxiously trying to judge the atmosphere 19 months from now, at the 1982 elections, after the cuts have actually been in effect a year. Most of the House Democrats seem to be inclined to bet that voters will still be insisting on tighter spending, but, by then, their enthusiasm for the cuts will be less indiscriminate, and some second thoughts will be emerging.

But those are only very tentative judgments. At every stage in the passage of this budget, it is going to be sharply affected by any hint of change in the climate, not here in Washington but, as congressmen say, back home.