PUTTING together a budget for 1983 has been predictably difficult for Congress this spring. Over the summer, the process is going to get much more difficult--and less predictable.

Negotiators for the House and Senate have now agreed on their first budget resolution--the outline that sets targets and orders committees to come up with legislation. The next step isn't likely to go quite so rapidly as it did last year. For one thing, the congressional awe, and even fear, of Mr. Reagan has dissipated. For another, the budget now moving through Congress is not Mr. Reagan's. The Republicans dropped that one early on grounds that the deficit was too high. The budget outlined in this first resolution is, in fact, several notches tighter than the one that the president offered in February.

Above all else, Congress was cutting taxes last year. This year, it has to raise taxes. The House Ways and Means Committee, with its Democratic majority, appears inclined to require the Senate Republicans and the president to commit themselves firmly to the increases before it moves. So far, there is not a glimmer of an agreement regarding which taxes to raise. The resolution says only that the result has to add up to $21 billion in new revenues. There was almost that much proposed in the original Reagan budget of last February, in a long series of minor provisions. But much of that list was patently unrealistic, and the president has already renounced some of it. Congress is going to have to do better, although it is already very late in the year to begin.

Some of the reductions in spending will be even harder--the $3.6 billion to come out of Medicare, for one prominent example. A highly organized and emotional lobby stands vigilant guard over Medicare. Then come the further cuts in Medicaid, food stamps and the rest. It's one thing to put these figures into a resolution. Actually to pass the legislation is something very different.

But don't blame the formal budget procedures. They are only making Congress come to terms with the gross mistake that it made last year, when it passed a tax cut that was far too large. The remarkable thing in the current session is that the budget procedures have continued to operate at all. So far, the budget has been driven forward solely by the deep reluctance of just about everyone in Congress to bear the blame for a breakdown. The Democrats have been understandably sensitive to the president's suggestions that they were responsible for the delays and, consequently, for the high interest rates being imposed by nervous lenders. They decided that, with an election campaign ahead, it was mandatory to get a first resolution enacted. It is by no means clear that this logic will be enough to push through the bills that now must follow--most particularly, the tax bill.