IN the month-long speculation about Cabinet appointments, there wasn't much about the Department of Health and Human Services (HHS -- before its recent amputation, known as HEW). Yet it is on this department's turf that the Reagan administration may have to fight its toughest battles for budget control. Shorn of its education responsibilities, the department is still the biggest and fastest growing spender of federal dollars of all the departments, including Defense. This year it will spend about $220 billion, well over a third of the budet and over 45 percent of non-defense outlays.

It's not just the magnitude of its budget but the peculiarities of its programs that makes HHS a super-tough management job. Most of HHS dollars go to the so-called "uncontrollable" programs that guarantee cash and other benefits to various citizens. Cutting these programs requires changing their basic terms -- who is eligible and what he gets -- which is a long and intricate process at best. HHS budget reductions can be painful for states and localities as well, since HHS grants-in-aid are the single largest source of oustide money for many of them.

A quick review of some of the major HHS programs shows how complex thte new secretary's agenda will be. Over half of the HHS budget goes for Social Security cash payments. No one is talking about cutting these benefits right now, but there are tricky questions involved in financing the program in the next few years.

And there is Aid to Families with Dependent Children -- what most people mean by welfare and what most people think of first when it comes to controlling government spending. But, in fact, the number of people getting AFDC has actually declined in recent years, and action here is likely to focus on proposals to turn major responsibility for the program back to the states -- a gift that both welfare recipients and the states themselves may well view with a cold eye.

The toughest problems of HHS management could be the major medical assistance programs, Medicare and Medicaid. These programs will cost over $50 billion this year and continue to grow much faster than prices in general. The sticking point in this area, as other secretaries have found, is that the troublemakers are not so much the recipients of the benefits -- the aged, poor and disabled -- as the doctors, hospitals and other health care providers -- an even tougher group to control, especially for an administration opposed to direct regulation of medical prices and services.

Trying to tackle these "uncontrollable" giants, as well as the rest of the more than 200 programs that HHS directs, has been the undoing of more than one able and determined secretary. We don't say it will be the undoing of another. This is just a friendly reminder that the Cabinet position that has been so little in the news until now is the one to keep your eye on.