THE SIZE of your next hospital bill is the subject of the current quarrel in the House Commerce Committee. President Carter wants to put the hospitals under firm cost controls. Congress, which has become leery of controls in general, is resisting. The hospitals, needless to say, think that mandatory controls are a terrible idea and say that they can do better through voluntary restraint. The House seems to be moving uneasily toward a compromise giving a trial to voluntary restraint, with mandatory controls to go into effect if it fails. But whether there are the votes to get that compromise out of the Commerce Committee is still an open question.

Perhaps you don't much care how large your next hospital bill might be if, like most Americans, you don't expect to pay it directly. If you are elderly or poor, the government will pay. If you or someone in your family is employed, you are probably covered by a group insurance plan. But insurance coverage in this country is far from complete. And even if you do not pay directly, you certainly pay indirectly.A typical family of four, earning $16,000 a year, contributes about $2,000 a year to the support of the American health-care system. This family is not aware of the scale of the outlay, of course, for it is levied through various taxes plus the health-insurance premiums that an employer pays. But it's a real cost, and rising rapidly.

President Carter is firmly committed to enacting a comprehensive national health-insurance program. The White House is to send an outline of the plan to Congress this month. The chief obstacle to that kind of plan is a widespread, and justified, fear that it would incite even faster inflation in health-care costs. The AFL-CIO argues that no effective cost control is possible without national health insurance. But most other people take the opposite view: that cost controls will have to be established before it is safe to proceed with comprehensive insurance.

The political dilemma here is demonstrated by the AFL-CIO. It is a powerful and deeply committed advocate of national health insurance. But it is against the hospital cost control bill. It fears that the costs will be controlled mainly at the expense of hospital workers who are paid the leats - that controls will hold down the wages of the kitchen and laundry help, not the salaries of the doctors and administrators. The unions argue that controls ought not include labor costs at all, since hospital payrolls are not rising nearly as fast as other expenses.

The combined opposition of the hospitals and the labor unions is the reason for the extreme difficulty in finding votes for the compromise bill in the Commerce Committe. What would happen if no bill is passed? The American Hospital Association points out that hospital expenses rose 15.6 per cent last year, but the annual rate dropped to 13 per cent in the first three months of this year. That, it says, shows that voluntary restraint is beginning to work. But it's also possible that the threat of stronger measures is having a certain effect. In any case, hospital expenses are still rising intolerably fast.

A bill is necessary, and the present compromise bill is right in principle. A trial period for voluntary compliance is worth trying. A trial period for voluntary compliance is woth trying. A recent experience has shown, legislated controls are horrifying complex, and there's never any guarantee that they will work effectively. But it needs to be acknowledged that this kind of bill means a delay, and perhaps quite a long one, in the enactment of national health insurance. It can't be passed until medical cos controls are in place, and the country can see it demonstrated that they are in good working order.