Correction: An earlier version of an information box with this article about upcoming Supreme Court cases incorrectly said that the case of United States v. Jones was brought by a convicted D.C. drug dealer. The U.S. government is the petitioner in the case, which involves GPS surveillance by police. This version has been corrected.

The Supreme Court convenes Monday for what could be the most significant term of Chief Justice John G. Roberts Jr.’s six-year tenure, with an agenda that both reflects the nation’s political landscape and offers the potential to reshape it.

The dominant theme is the one that has divided the country and fueled the debate between tea party Republicans and President Obama since the 2010 election: the extent of the federal government’s power.

The justices are being asked to decide the constitutionality of the landmark health-care act, the ability of states to enforce strict immigration laws and whether the government can continue to monitor the airwaves for indecency.

The court could also reopen the question of affirmative action in college admissions, rule on the rights of gay adoptive parents and decide whether the blindingly fast pace of modern technology has reshaped Americans’ notion of privacy.

“Whatever the last term lacked in blockbuster cases, here’s one that’s really for the ages,” said Paul D. Clement, solicitor general in the George W. Bush administration.

Clement will play no small part in the term’s deliberations. He represents the states challenging the Affordable Care Act and will defend Arizona’s tough anti-immigration law, whose most controversial parts have been blocked by lower courts.

The potential of the term, said Steven R. Shapiro, legal director of the American Civil Liberties Union, is not measured in the cases the court has already accepted but by “what the court might take.”

And while justices recoil from the idea that politics play a role in their decisions even to accept a case, it is clear that the court’s actions this year will be scrutinized through the lens of an election year.

Partisan groups on both ends of the political spectrum increasingly analyze the justices’ public speeches, private finances and past affiliations to highlight what they see as bias. Another goal is to seek their recusal in controversial cases.

Liberal groups and some Democratic members of Congress are seeking investigations into Justice Clarence Thomas’s failure to list on financial-disclosure statements that his wife, Virginia Thomas, was employed in the past by conservative organizations opposed to the health-care law. Her work was common knowledge at the time, and he has since corrected the forms.

Conservative groups question how involved Justice Elena Kagan was in forming the Obama administration’s legal defense of the health-care law when she was solicitor general, the government’s chief appellate lawyer. Kagan said during her confirmation hearings she did not play an active role.

Justices decide for themselves whether they have a conflict that requires recusal — there is no mechanism for replacing them if they do — and there is no indication that either Thomas or Kagan will opt out of deliberations on the health-care act.

It would be highly unlikely that the court would not accept the Obama administration’s request to review conflicting lower-court decisions on the constitutionality of the centerpiece of the health-care law, the “individual mandate” that requires virtually every American to carry health insurance.

But there are options that could make it a narrow decision rather than a broad constitutional ruling.

A decision on the health-care law “could turn out to be transformative or could turn out to be a fizzle,” said Pamela Karlan, a constitutional expert at Stanford Law School.

Most also believe the court will take the Arizona immigration law, as well, which is being replicated in other states. The Obama administration also has sued the state of Alabama over its law — saying control of the nation’s borders is exclusively a power of the federal government — and is deciding whether to challenge four other states.

The government is defending the authority of the Federal Communications Commission to police the airwaves during the times when children are most likely to be watching. The broadcast networks are challenging the FCC’s rules as unconstitutionally vague and outdated when cable television and the Internet are unregulated.

The case involves FCC fines for network shows in which celebrities used profanities at award shows and the old television drama “NYPD Blue,” which showed a woman’s bare buttocks.

The U.S. Court of Appeals for the 2nd Circuit in New York ruled against the FCC, saying its rules showed “little rhyme or reason.” The government claims it should be allowed to keep the broadcast channels as a “safe haven” for families.

Changing technology is at the heart of another case that weighs government’s power to track suspects against an individual’s right to privacy. The question is whether the government has the right to place a Global Positioning System device on the vehicle of a suspected drug dealer without a judge’s approval. The Justice Department points to a Supreme Court ruling to say citizens have no reasonable expectation of privacy as they travel along public streets and highways.

But the U.S. Court of Appeals for the D.C. Circuit disagreed. It said 24/7 monitoring of a person’s whereabouts for an extended period requires a warrant. Other courts of appeal answered the question differently.

The affirmative action case that may get the court’s attention is from the University of Texas, where officials take into account a student’s race to try to make the student body more reflective of the state’s population.

An appellate court panel said such an approach was in line with the court’s last major decision on the use of race in the admissions process, which came in 2003. But the Supreme Court has become more conservative since then — most notably because of the replacement of Justice Sandra Day O’Connor by Justice Samuel A. Alito Jr.

Conservative legal groups are urging the court to take another look at the issue.

And while it is unclear if the issue of gay rights will make it onto the court’s agenda this term, it is coming. Legal fights over California’s Proposition 8, which bans same-sex marriage, and the constitutionality of the federal Defense of Marriage Act continue in the appeals courts.

One case already seeking grant by the court involves a New York same-sex couple who adopted a child in Louisiana and were denied a request that both of their names be on the child’s birth certificate.

On the docket

Zivotofsky v. Clinton: A major separation-of-powers case that asks whether the president may ignore Congress’s directions. The case is brought by an American couple who want their son’s birthplace listed as “Jerusalem, Israel” despite State Department objections.

United States v. Jones: Do police need a warrant before attaching a Global Positioning System device to a person’s automobile to track him 24 hours a day for weeks?

FCC v. Fox Television Stations Inc.: Are the Federal Communications Commission’s standards for indecency on television too vague to meet constitutional standards?

Awaiting action

HHS v. Florida: Does the Constitution’s Commerce Clause give Congress the power to require Americans to obtain health insurance?