STARTING LAST TUESDAY afternoon, daily live coverage of the House of Representatives became a part of the television fare available to several million Americans. These are the viewers whose sets are hooked up to one of the 370 cable television systems getting a signal beamed from Northern Virginia via satellite. For most people, though, live coverage of the House will remain an occasional event. It won't be available unless commercial or public TV stations deem the day's proceedings important or lively enough to compete with their regularly scheduled fare.

By that test, of course, the House proceedings sink without a trace most days. They are so dull that even large numbers of the people who participate in them can't bear to sit there to the end-never mind how the viewing audience would feel. But the availability of these proceedings to those who might want to watch underlines the potential of cable television: It can, if it will, provide subscribers with a range of programming far broader than conventional TV stations.

It is for this reason that the Dederal Communications Commission three years ago ordered large cable systems to develop the capacity to handle at least 20 channels and to reserve some of those channels for use by local governments, educational institutions and the general public. This was a way of making cable TV live up to its potential and of trying to ensure that the size of its wires does not seeon become the limiting factor on the amount of information that can be transmitted into homes.

When the Supreme Court ruled Monday that the FCC lacked the power to issue those orders, it did not leave a void. State and local governments are still free to regulate cable television, and Congress can, if it wants to, give the FCC the power the court says it lacks. This last course, however, seems unlikely, since a move is already afoot in exactly the opposite direction: to free cable television from all federal regulation.

What is important is not so much who regulates the cable systems but how the systems are regulated especially in terms of capacity and access. State and local governments may be able to protect the public interest, but only if they are as perceptive as the government in Arlington, which negotiated the franchise now bringint cable to the county. The coincidence of the court's ruling and, a day later, the routine appearance of the House of Representatives on television screens in all 50 states may help train attention on what is bound to become a serious argument over this country's prospective communications network.