A PRISON inmate who found his scrambled eggs too firm for his taste sued the Massachusetts Department of Correction on the grounds that the miscooked dish constituted cruel and unusual punishment.An eight-year-old in Miami, Margo Mankes, who said she was bored by the Girl Scouts, filed a sex-discrimination suit against the Boy Scouts of America. Her lawyer argued that her exclusion from a Scout camp caused her to suffer "irreparable damage." Americans have tended to be quick on the draw to sue. But never before have so many citizens discovered their rights and decided to stand on them. Access to a day in court is one of the most precious and fundamental guarantees that democracy offers. Furthermore, it is impossible to say what far-reaching good may result from a small stand on principle, as on that day Rosa Parks refused to go to the back of the bus. But an overloaded court system is on a collision course with the increasingly popular notion that for every grief in life someone else is legally responsible and must be made to pay. Something has to give. The federal court budget rose from $1.42 billion in 1988 to $2.59 billion in 1991. Cities on the verge of bankruptcy are paying out hundreds of millions of dollars a year in damages because they are such convenient targets: New York City recently was sued for negligence by a drunk who fell onto subway tracks and claimed the municipality was responsible for his injuries because the law says an intoxicated man should be expelled from the subway. Still, the financial cost of litigation is the least of it. The proliferation of cases has produced a situation known as "legal gridlock." One-third of civil suits are more than a year old before they reach court. And the frivolous use of the courts comes at the expense of criminal cases. The backlog of drug cases in federal courts rose to 7,400 at the end of 1990, up from 1,200 at the end of 1989. What can be done to relieve the pressure? In a 5 to 4 decision last month, the Supreme Court gave federal judges broad powers to fine plaintiffs and defendants who abuse the system by trivial suits or obstructive tactics. Some observers want more cases confined to lower, local levels of the courts. But such restrictions can be dangerous. Justice by nature is slow rather than efficient. A promising alternative to civil suits is the increasing use of mediation and arbitration. In 1990 an estimated 615,000 potential court cases were settled by one form of "alternative dispute resolution" or another. Here is a delicate dilemma - making recourse to the courts available to all, while cultivating the discipline to keep lawsuits from being the first, knee-jerk reflex when a dispute or almost any kind of hardship occurs. How to do justice to the justice system? This question, worthy of a Solomon, must take priority on the docket if the courts are not to forget the true purposes of justice and sink, like many a bureaucracy, under their own weight.