The tricky precedent is the Eldred case by which the Court had upheld Congress' power to extend copyright terms beyond those originally permitted when a particular work qualified for copyright protection. That case had been argued primarily on a theory that the "progress clause" of the constitution (that Congress shall have authority to enact copyright laws to promote the progress of the arts, etc. for limited times) prohibited repeated extensions that effectively made the copyright terms permanent and hence not for "limited times" only. The Court had rejected that argument in a 7-2 decision.
Here, EFF distinguishes Eldred by arguing that, while Congress may have the power to extend rights of existing copyright holders, it lacks the power to restore to a copyright holder rights to works of authorship that no longer belong to them but are instead in the public domain. That is, such "restorations" do nothing to further the progress of the arts (the constitutional justification by which Congress can enact such laws) and, even if they do, are nonetheless constitutionally defective because they violate free speech rights of those who seek to express themselves in a vibrant public commons consisting of public domain works available to all.
The legal nuances here are tricky but it is highly encouraging that the Court decided to grant certiorari in this case. Liberals have long argued for virtually unlimited powers for Congress in enacting statutory laws while conservatives have basically rubber-stamped such broad powers when it comes to expanding IP laws and the Court's factions have tended to follow these broader trends. In a digital age, this means basically that those who can "persuade" Congress to enact pet legislation favoring their commercial interests have an open ticket to extend their protections far beyond what was properly intended by copyright laws, among others. Perhaps this case will begin to draw a line or two that says, "enough is enough." It will be interesting to see it play out. Kudos to EFF for being at the forefront of this fight.