Helmut Schmidt's coalition survives, but for how long?

Chancellor Helmut Schmidt's uneasy coalition government has survived its most serious crisis so far by agreeing on a budget for 1983. But the sense of relief may not last long.

The bruising weeks of argument which preceded the June 30 last-minute accord have drained much of the remaining energy from the 13-year-old ruling alliance of Social Democrats and Free Democrats.

And much of the time, the debate seemed to be less about the precise level of the federal borrowing requirement than about how to bring the coalition to a decent end.

Up to the last minute, West German newspapers were full of speculation and scenarios for the collapse of Mr. Schmidt's government. The Free Democrats, alarmed by recent regional election defeats for the coalition partners, would use the budget talks as a pretext to switch to an alliance with the opposition Christian Democrats, the papers predicted.

Ambivalent remarks by Foreign Minister Hans-Dietrich Genscher, the Free Democratic leader, helped fuel such speculation. His call for a ''turning point'' in government policy was widely interpreted as the opening shot in a final battle with the Social Democrats.

But the Free Democrats' constant wavering, combined with running debates with the Social Democrats over nuclear arms and energy policy, produced a situation in which the coalition seemed unable to govern firmly or draw honorably to a close.

Part of the problem lay with the parliamentary opposition. Christian Democratic leader Helmut Kohl, who would probably become chancellor if Mr. Schmidt fell, is seen as a somewhat colorless figure. His party has not been proposing policies which might make change easier.

In fact, they have hardly made any policy proposals at all and diplomats trying to predict to their governments what might be different under a Christian Democratic-led administration in Bonn have been hard pressed to find much difference from the present policies.

Mr. Schmidt told reporters after the budget agreement was concluded that he now expected the coalition to last until the next elections in 1984.

But many political commentators believe the deal will only carry the government through until the next crisis in September, when it faces the possibility of another demoralizing defeat in a regional poll in the state of Hesse.

A Christian Democratic victory in the state - the most likely outcome at present - would give the opposition a two-thirds majority in the Bundesrat (upper house of Parliament), enabling it to block all major legislation.

The Christian Democrats could then use this power to veto some of the cuts in tax privileges for the well-to-do with which the government hopes to limit next year's budget deficit. Also in September, the government receives the latest forecasts for economic growth and unemployment next year.

The 251 billion mark ($104 billion) budget which was just approved has assumed economic growth of about 3 percent in 1983 after inflation is discounted with average unemployment of 1.85 million over the year. Both Finance Minister Manfred Lahnstein and Economics Minister Otto Lambsdorff have already acknowledged that these predictions could be too optimistic, especially if high US interest rates continue to depress the world economy.

''By late September, the government could have been humiliated in Hesse and thrown back into another budget row. cl11It's not over yet,'' said one insider.

Another question which must be worrying Mr. Schmidt is how his own Social Democrats will react to the welfare cuts in the planned 1983 budget, approved grudgingly by Social Democrats parliamentarians this week. The party, which adopted calls for increased spending on antiunemployment measures at its national congress in April, seems certain to face protests from the grass roots at measures which raise unemployment insurance contributions and force patients to contribute for the first time to their own hospital costs.