By agreeing today to hear challenges to President Obama’s 2010 health care law, the Supreme Court set the stage for a decision — probably in late June and in the midst of the presidential campaign — that could be among its most important in decades.

The case, which will probably be argued in March on a date still to be announced, is especially momentous because it not only will determine the fate of President Barack Obama’s biggest legislative achievement but also will cast important light on the Supreme Court’s future course under Chief Justice John Roberts on issues of federal government power.

The central issue — but not the only important one — is whether Congress exceeded its constitutional powers to regulate interstate commerce and to levy taxes when it adopted the so-called “individual mandate” at the heart of the health care law.

That provision would require millions of people starting in 2014 to buy commercial health insurance policies or pay financial penalties for failing to do so.

The court also agreed to decide a challenge to the Affordable Care Act’s provision essentially requiring states greatly to expand their Medicaid spending.

The court made clear that if it decides to strike down the individual mandate or Medicaid provision, it will also decide which of the 975-page law’s hundreds of other provisions should go down too, by divining whether Congress would have wanted some or all of them to be effective even without the voided provision or provisions.

Finally, the court agreed to decide whether — as one federal appeals court ruled — the litigation surrounding the individual mandate must be deferred until 2015 because of the 1867 “Anti-Injunction Act,” which bars courts from striking down tax laws before they take effect.