Roberts said from the bench that the court's last day of the term will be Thursday, and that all remaining opinions are expected to be issued that day. He did not specifically mention the healthcare case.
The court's ninth member, liberal Justice Elena Kagan, did not take part in the immigration ruling - believed to be because she worked on the case in her prior job as Obama's solicitor general.
Last year, the court upheld a different Arizona law that penalizes businesses for hiring illegal immigrants.
Obama on June 15 announced an important change in U.S. immigration policy. Hundreds of thousands of illegal immigrants who were brought into the United States as children could be able to avoid deportation and get work permits under the new policy.
The Supreme Court case is Arizona v. United States, No. 11-182.
(Reporting by James Vicini, Joan Biskupic and Jonathan Stempel; Editing by Howard Goller and Will Dunham)