The paper - "Grossly Excessive Penalties in the Battle Against Illegal File-Sharing: The Troubling Effects of Aggregating Minimum Statutory Damages for Copyright Infringement" by J. Cam Barker argues that the file sharers sued by the RIAA have a
constitutional right to pay much smaller penalties than the millions of dollars they can be liable for under copyright law's minimum damages of $750 per song.

In the authors own words:

In this paper, I argue that there is a constitutional right to not have a highly punitive statutory damage award stacked hundreds or thousands of times over for similar, low-reprehensibility misconduct. I point to the rationale behind criminal law's single-larceny doctrine, identify the concept of wholly proportionate reprehensibility, and use this to explain why the massive aggregation of statutory damage awards can violate substantive due process.

I conclude that massively aggregated awards of even the minimum statutory damages for illegal file-sharing will impose huge penalties and can be constitutionally infirm like the punitive damage award of Gore itself. Yet practical and institutional reasons will likely make this norm underenforced by the courts, pointing to Congress as the actor that should modify copyright law to remove the possibility of grossly excessive punishment.

You can download the paper here.