WHEN Richard Nixon established the Legal Services Corporation 21 years ago, he emphasized giving poor people better access to civil courtrooms and protecting that access from political interference. Today, some of his GOP descendants seem ready to ignore that message. They would like to ''block grant'' the nonprofit LSC, which now gets about $400 million a year from the federal government. It would then be up to states to sustain what they could of the LSC, which currently supports legal-aid centers throughout the country and spends a mere 3 percent of its budget on administrative costs in Washington. But block grants to states would only be temporary. Many in Congress want to eliminate all funding for the program over the next few years. Their grounds: that legal-services lawyers too often meddle in politics and that their work can be picked up by private law offices. Neither ground has much solidity. The class-action lawsuits that have particularly irked conservative critics are a tiny fraction of the work done by legal-aid offices around the country. Landlord-tenant disputes and consumer rip-offs are common fare. And about a third of the 1.7 million clients served last year needed help with family matters, including child custody and divorce. Those cases have fed another criticism - that legal aid has encouraged family breakups. But the cases typically involve abusive relationships that need to be ended. It's true that legal work for the poor often includes securing government benefits for clients, another thing that galls critics. But such benefits are crucial to low-income Americans. Congressional efforts to prevent legal-aid lawyers from suing governmental agencies would strip them of the ability to serve clients. And the contention that private lawyers will pick up the slack if legal services is phased out as a government program? That rests on the shaky proposition that lots of legal resources are just waiting to be utilized. In fact, the LSC is the means through which some 130,000 private lawyers a year do pro bono, or free, work for indigent clients. The various centers supported by the corporation link clients with lawyers and provide research backup. The American Bar Association estimates that the legal system, even with the Legal Services Corporation, meets only about 20 percent of the civil litigation needs of poor people. Legal services is on the brink of extinction in Congress. Next week, both the House and Senate will decide on bills that affect its future. Compromises such as a ban on class-action suits may not be enough to stave off the killing of the program. The LSC brings a significant measure of practice to American preaching about equal justice. It would be ironic if only those poor people who run afoul of criminal law - and thus have access to public defenders - end up with lawyers on their side. Even with the Legal Services Corporation, 80 percent of the poor's needs are not being met.