Just how much responsibility does the federal government bear to see that every willing student gets through college? And through which college? The Reagan administration's budget delivers a fundamental challenge to the whole haphazard structure of federal aid to students. It's not a well-crafted challenge; the administration has not carefully examined the implications for its own policies. In any case, Congress is unlikely to accept such drastic reductions. But those questions are the right ones to ask, and the conventional answers are very much due for an unsentimental examination.

Federal aid to college students, as it now exists in this country, is a peculiar accumulation of many different programs enacted at different times for purposes not always consistent with each other. You will grasp the essence of the thing if you look at it as a compromise developed over the years between the interests of the private colleges with high tuitions and the public colleges with relatively low ones. Congress, caught between the two lobbies, has added a little here and a little there to keep the total array of benefits from pushing hard in favor of either.

The administration proposes several kinds of limits on the current benefits, the most important being a ceiling of $4,000 a year on federal aid of all sorts to each student. The average cost of attending a four-year public college, including room and board, is currently about $4,900 a year, according to the College Board. The comparable cost at a private college averages $9,000. The administration's ceiling threatens the fragile balance that Congress has tried to strike between the two.

The newly installed secretary of education, William J. Bennett, vigorously defended the ceiling at a press conference earlier this week. The administration is saying here, he argued, that it wants to provide opportunities for students who might not otherwise be able to go to college at all -- and it will give preference to those students before it helps those who need more aid to go to more expensive colleges. That's the right way to frame the issue.

But it's a curious position for the Reagan administration to take -- an administration that has usually given great emphasis to the importance of the private sector and its alternatives to public services. In the field of education, the administration is now strongly supporting the concept of private alternatives to the public schools, but not to the public colleges.

There's a certain appeal to Secretary Bennett's argument. Perhaps federal aid to students ought to be keyed to the cost of attending only public colleges. It's an idea at least worth debating. But if you accept that proposition, does it not follow that the federal government has no business providing federal aid -- through vouchers and tax incentives, as President Reagan wants to do -- to private elementary and high schools?