Washington — Justice Sandra D. O'Connor, who breezed through her confirmation in the US Senate, now faces one of the Supreme Court's busiest times of the year as it prepares to open the new term next week.
During the summer recess more than 1,000 cases have piled up on the high court's docket, and the newest justice and her eight colleagues must determine which deserve their attention. On opening day, Oct. 5, they will announce no more than about 50 that will win a high court hearing.
Also on the agenda will be 102 cases that the Supreme Court has already agreed to hear during the coming months. They run the gamut from a challenge to the federal rules for presidential campaigns to the State of Florida's claim to 25 percent of the treasure brought up from a Spanish galleon that sank in 1662.
In past years one or two major cases have often dominated the court term, as with a spectacular, but unsuccessful, challenge to the all-male military draft registration last year or school desegregation suits, or the 1973 decision in favor of abortion rights.
So far no such overriding case has surfaced for the 1981 term of a Supreme Court that is widely seen as more cautious than that of the 1960s and early '70s and as more likely to defer to other branches of government, especially to Congress.
However, the cases already accepted touch virtually all facets of American life.
* As thousands of Mexicans cross the US borders illegally, Texas has answered this humanfloodtide by refusing to pay for their children to attend public schools. In Tyler, Texas, the school system charges illegal foreigners $1,000 tuition. Since few of the parents can afford to pay, it has effectively shut the children out of education.
Texas supporters charge that undocumented foreigners have no equal right to state benefits, but a US appeals court has thrown out the Texas law as discriminatory and "harsh." In what will probably be a major ruling this term, the Supreme Court is slated to decide which side is right, and the result will have a powerful impact on both the immigrants and the US Southwest.
* In a dispute that will be argued the second week of the term, a student group at the University of Missouri has been forced off campus because it held religious services. Religion studies are permitted, but worship is not, according to university regulations that draw the separation between church and state.
* Reforms for election campaigns face an assault from independent political groups that collectively spent millions to back Ronald Reagan's presidential campaign. They are charging that the Federal Election Commission (FEC) violated their constitutional rights to free speech by limiting them to spending only $1, 000.
The political groups say the limit should apply only to committees authorized by the candidate, but the FEC counters that the $1,000 control is necessary for all groups, so that it can prevent corruption and pressure from private campaign funding.
* The Supreme Court may set important new guidelines for how states may take cildren away from their parents. John and Annie Santosky of New York lost all parental rights to three of their children because a court found them unfit parents. The couple is now charging that the court used too lenient a standard for judging evidence against them.
Last term the court began to move into the parental rights area when it found that poor parents are not entitled to free attorneys in parental rights cases.
* The court will continue its case-by-case review of capital punishment by looking at a plea from Monty Lee Eddings. At 16, Eddings had a fight with his parents one evening and then left home, taking a shotgun and a rifle and automobile with him. On his drive through Oklahoma, a highway patrolman approached his car, and the teen-ager fired the shotgun, killing the officer. Eddings was tried as adult and sentenced to death, a penalty his lawyer says is "cruel and unusual" for a 16-year-old.
The last reported execution in the US of a 16-year-old was in 1949.
* In a major job discrimination case, the court is being asked to decide whether schools that accept federal aid must prove that they do not discriminate against women employees, as well as women students. The University of Seattle is claiming that the US Title IX rules on sex discrimination apply only to treatment of students.
Also this term the court will consider disputes over whether the public has access to the Princeton University campus, over the venting of radioactive steam at the Three Mile Island nuclear plant, and over a cable television agreement in Boulder, Colo.