FOR most Americans, cities are the government that directly affects them. Cities provide water, schools, and basic social services. They pave and plow the streets. It would be nice if cities could pay their own way. But for decades, many have been caught in a Catch-22: Their tax base declines while the demand for services rises. And if they raise taxes to maintain services, more businesses and individuals flee to the suburbs, making matters worse. So the cities need help from the state and federal governments. State politics, however, often preclude increased aid to cities: Outstate legislators know voters aren't keen to pay increased taxes to what the voters often see as corrupt and inefficient city governments. Sometimes, unfortunately, race is a factor, too. The federal government has thus been the funder of last resort, and often furnishes large percentages of city budgets. But those budgets, already lean, would take an inordinate hit if the US Senate doesn't modify budget-cutting bills passed by the House. Mass-transit, crime-prevention, education, and job-training funds are among those scheduled for trims. A recent survey of mayors, Democrats and Republicans, found that 96 percent of those responding believe the cuts will have a negative impact on their cities. More than 80 percent said they would have to reduce city services, and more than 40 percent said they would have to raise taxes. Here's how the House proposals would affect Boston, based on comparison with the fiscal 1995 budget: * Education funds for disadvantaged children, down $4 million or 18 percent. * Funds for summer jobs, job training, and dislocated workers, down $2.8 million or 51 percent. * Public housing, homeless assistance, and antidrug funding, down $27.5 million or 26 percent. * Energy assistance to the poor and elderly, completely eliminated. In addition, cities are already staggering under unfunded federal and state mandates. If their funding is cut without relief from these requirements, they will end up with the worst of both worlds. Cities must take their share of trims along with everyone else in a time of budgetary restraint. But the House cuts are too severe. By adding less to the defense budget and going easy on tax cuts, Congress can reduce the deficit and still help the cities. In addition, federal and state lawmakers should immediately begin reviewing and eliminating unfunded mandates on local governments. Republicans everywhere should have no quarrel with that. By adding less to defense and going easy on tax cuts, we can reduce the deficit and still help the cities.