The natural-gas bill, which comes to a head in the Senate this week, provides a test of the system. For Jimmy Carter is making support of the measure a vote of confidence in the presidency and its special role in developing comprehensive solutions to grave national and international problems.

His opponents are a collection of diverse, even warring, interests primarily concerned with the particulars of the measure. By pitting the center against the peripheries, the gas bill raises once again the issue of governability that has dogged national affairs since Watergate.

The administration acknowledges that the present bill, a compromise that has scraped through both Houses of the Congress and the House-Senate conference, is not perfect. But it claims the bill does address three major problems. One is the shortage of natural gas in the Northeast and Midwest. Such shortages caused factories and schools to close down during cold-weather periods in the past two winters.

Second is an excess of natural gas in the main producing states - Texas, Louisiana and Oklahoma. The absence of price controls on intrastate gas has elicited so much of the stuff in the producing areas that Texas, at least, is now restricting production.

Finally, there are oil imports and the adverse impact they have on the balance of payments and the health of the dollar. More abundant natural gas would make it possible to cut down on some oil imports.

The compromise bill would meet those objectives in the following way: Price controls, which now cover only interstate gas, would also be extended to intrastate gas. The price for newly discovered gas, now $1.50 per thousand cubic feet, would be raised to $1.93 right away and allowed to go up in stages until all price controls were lifted in 1985.

The $1.93 price allowed nationally would exceed the present price - about $1.80 - in the producing states. That, according to the administration, would immediately make available for the whole country a trillion feet of natural gas now being held as excess in the producing states. As a result, gas could be substituted for imported oil. Imports could be cut by nearly half a billion dollars a day at once, and eventually, as rising prices elicited rising production, by nearly 2 million barrels daily. Thus President Carter would fulfill the pledge he made to the other leaders of the industrialized countries at the Bonn summit last July.

Against these arguments there have been mobilized two big - and diametrically opposed - groups. First there are the producers, who feel that the proposed legislation, while acceptable on price, hamstrings them withan impossible tangle of regulations as to what gas fits into what category. Their case has been argued vehemently by a number of lesser known Republican senators - including, Dewey Bartlett of Oklahoma and Clifford Hansen of Wyoming. But it has also attracted the support of a number of Democratic heavies who usually like to work with the president - among them, Russell Long of Louisiana and Lloyd Bentsen of Texas.

Joining them in opposition from another angle are the consumers, who object to paying higher prices for gas at a time of rising inflation and when there is plenty of gas available. Their view has been strongly pushed by two Democratic liberals - Howard Metzenbaum of Ohio and James Abourezk of South Dakota. But they have als been joined by some heavyweights - notably Edward Kennedy of Massachusetts and Ernest F. Hollings of South Carolina.

The balance of power is probably going to be held by the moderate Republicans. Minority Leader Howard Baker has declared against the bill - for another parochial reason, namely, that it makes no provision for building an advanced nuclear installation in his home state of Tennessee. If Baker fights really hard, and brings a cluster of Republicans with him, the administration will lose.

An administration defeat would not be disastrous. For the opposition forces, though conceding norhing to Carter's pledges to allied leaders, would give the president emergency powers to distribute intrastate gas on the national market in the event of a bad shortage.

Even so, I hope Carter wins on this one. As an institution, the presidency needs all the support it can muster these days. But I also hope that in the future Carter will invoke presidential prestige only for far better causes. For there is a governability crisis in the country. Presidential power is at hazard, and it ought not to be risked on measures that do not attract the support of the most widely respected senators.