WASHINGTON — The Supreme Court on Monday agreed to hear a challenge to the 2010 health care overhaul law, President Obama’s signature legislative achievement, setting the stage for oral arguments by March and a decision in late June as the 2012 presidential campaign enters its crucial final months.

The decision to hear the case prompted confident assertions from each side that it was sure to prevail, and gave rise to calculations about the complicated political impact of possible rulings.

The range of issues the court agreed to address amounted to a menu of possible resolutions: the justices could uphold the law, strike down just its most controversial provision or some or all of the rest of it, or duck a definitive decision entirely as premature.

Whatever the outcome, the tensions running through the case — between the 26 states challenging the law and the federal government, and between Mr. Obama and the Supreme Court led by Chief Justice John G. Roberts Jr. — are likely to give rise to both a political and constitutional blockbuster.