Do The Statutory Damages Rates For Copyright Infringement Violate The Eighth Amendment?

While we often discuss the rather large conflict between the First Amendment and copyright law in the US, Stephan Kinsella is also wondering if the current statutory damages rates in copyright also violate the Eight Amendment and its prohibition on "excessive fines." I somewhat wonder if that issue will come up in the Jammie Thomas appeal, which will focus heavily on whether or not an...