WHEN SENATORS cast their votes on the balanced budget amendment, as they are scheduled to do today, they might want to give some thought to their counterparts in state legislatures. Many senators are already having second thoughts about the wisdom of writing such dubious arithmetic into the nation's most fundamental document. Yesterday's addition of a requirement that even a rise in the debt ceiling--a perennial necessity for running the government--be approved by three-fifths of Congress should add to their concerns. It should also add to the concerns of state governments, which have been little consulted in the process thus far.

The easiest way to live up to the terms of the amendment would be, of course, to shift federal responsibilities to states. The administration's budget cuts have already shifted some burdens, and states don't like it. If the amendment seems to require more of the same, it may be headed for trouble in state legislatures, 38 of which must ratify it to make it part of the Constitution.

The people who drafted the first Senate version of the amendment recognized this conflict when they added a provision that no additional responsibilities could be cast off on states without federal money to pay for them. After thinking about the implications of this "hold-harmless" assurance, however, the amendment's authors changed their minds and deleted it from the version sent to the floor--without consulting the governors.

One of the things worrying the amendment's sponsors was that the prohibition would prevent the federal government from continuing to enforce existing federal laws that require states to spend their own money on such things as pollution control and education of handicapped children. Another concern is that further progress toward a balanced budget won't be possible unless additional responsibilities are pushed off on the states. Given the administration's determination to push for ever more massive military spending--and its resistance to raising taxes--there is simply no other way.

States, however, have good reason to be wary of a constitutional requirement that federal revenues and spending be balanced except in time of war. The current recession and federal budget cuts have already put many states into serious financial trouble. This year, 20 states have raised existing taxes or added new ones. State services are shrinking, payrolls are being cut and, at a time when many local roads, highways, bridges and sewer and water systems are in disastrous shape, construction and maintenance projects are being canceled.

The difficulty of financing swelling unemployment benefit rolls provides perhaps the clearest lesson about the danger of shifting national responsibilities to state and local tax bases. Hard-hit states have already borrowed over $2 billion from the federal government this year to cover unemployment benefits and by the end of the year, borrowing--including past unpaid debts--may reach $10 billion.

This borrowing wouldn't be possible if the balanced budget amendment were in place. Some states have already cut benefits and raised employer taxes, but they are afraid that further taxes will simply cause employers to move to other states and thus add to their unemployment burden.

There is no question that part of the states' current fiscal dilemma comes from their own lack of discipline in the past. But there is also real reason for concern that a federal retreat from national responsibilities could force states into a tailspin in future recessions. In explaining its own enormous departure from its avowed belief in balanced budgets, the administration cites the economy's current structural difficulties. But this will not be the last transition that the economy must weather. Putting the federal budget into a constitutional straitjacket would mean that in the next downturn, the states that bear the hardest burden will be thrown back on their own dwindling resources for relief.