For the first time in a decade, America's armed forces are having trouble meeting their recruiting quotas - a problem sure to become increasingly serious.

A manpower report for the first three months of fiscal 1989 - October through December - showed that the Army missed its quota of 24,143 by 475 men and women. The other services achieved their goals, but with difficulty.The shortfall in numbers is not all that great, but a more serious problem is the way the armed forces tried to meet their quotas. Both the Army and Navy were forced to take more Category 4 people - those who scored low on the military entrance test. In the Army's case, nearly 11 percent of the new recruits were from this less capable group.

Two things are causing the problem. One is the relatively healthy state of the economy. Unemployment is at a 14-year low, a factor that always affects enlistment in the armed forces. A second and more intractable problem is the dwindling supply of 18-year-olds in the population.

Taking more Category 4 people hurts the services, especially since nearly all parts of the military depend heavily on high-tech equipment. Trying to operate the system with people who do poorly on the entrance test is asking for trouble.

One way to resolve the shortage is to offer better pay and more benefits. But that can be difficult when the government is trying to cut the federal deficit - and do it in large part by freezing or reducing military funding.

Yet, as numbers of young people shrink, there will be increasing competition between business and the military for badly needed workers and soldiers, particularly ones that are capable and educated.

A last resort would be to bring back the draft. While that would solve the manpower problem, it would raise a great many others. It would be unpopular among young people, among society generally, and would be seen as political dynamite by Congress and any administration. Even military leaders tiptoe around the idea.

But this is an issue that will have to be faced, one way or another, in the next few years. It's either going to be expensive or politically awkward - perhaps both at the same time.