The justices probably will decide in the fall whether to resolve competing lower court decisions about the new health care law's requirement that employer-sponsored health plans include coverage of contraceptives.
An issue with a good chance to be heard involves the authority of police to search the contents of a cellphone found on someone they arrest. Justice Ruth Bader Ginsburg said over the summer that the right to privacy in the digital age "is bound to come up in many forms" in the years ahead.
The court may hear its first abortion case since 2007, a review of an Oklahoma law that would restrict the use of certain abortion-inducing drugs such as RU-486.
The campaign finance argument on Tuesday is the first major case on the calendar. The 5-4 decision in the Citizens United case in 2010 allowed corporations and labor unions to spend unlimited sums in support of or opposition to candidates, as long as the spending is independent of the candidates.
The new case, McCutcheon v. Federal Election Commission, is a challenge to the overall limits on what an individual may give to candidates, political parties and political action committees in a two-year federal election cycle, currently $48,600 to candidates and $123,600 in total. The $2,600 limit on contributions to a candidate is not at issue.
Since the Buckley v. Valeo decision in 1976, the court has looked more favorably on contribution limits than on spending restrictions because of the potential for corruption in large contributions. The big issue in the current case is whether the justices will be just as skeptical of limits on contributing as on spending.
Three justices, Anthony Kennedy, Antonin Scalia and Clarence Thomas, have signaled their willingness to do so. It remains to be seen whether Roberts and Justice Samuel Alito, the other two members of the Citizens United majority, are willing to go along.