If you're going to use the Constitution to justify these laws, you would be better advised to use the portion, also under Section 8 of Article 1 (Paragraph 8) which states
To promote the Progress of Science and useful Arts by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries.
and Paragraph 10
To define and punish Piracies and Felonies comitted on the high Seas, and Offenses agasing the Law of Nations.
Unfortunately, the internet is not the "high Seas" and copyright infringement is already against the law.
What this law and others like it are attempting to do is to regulate access, through the internet, to web sites and their offending content. The approach being used is another expansion of government power through the already grossly over expanded commerce clause.
The salient question is again, exactly how much of our liberty we are willing to surrender in the advance of the protection of property rights? We have already witnessed a tremendous expansion of the original charge contained in Paragraph 8 of the Constitution. The original authorization was "for a limited time." We have seen over the last century and expansion of that protection beyond the original protective laws.
The original copyright laws covered 14 years with an extension for an additional 14 years if the author survived the first 14 years. With the expansion of copyright coverage from books to all intellectual property, the term under international treaty was expanded to a minimum of 50 years from the date of creation.
So we see that these laws protecting property have been in existence a long time and were considered important as protections of personal property (a concept that was paramount in the minds of the Founding Fathers).
The problem arises not in these protection provisions, but in the means of enforcement which are now being considered. Once one begins to regulate the free traffic of ideas across the internet with the intent of protecting private property, then one has crossed from protecting intellectual property into restricting the free flow of information.
You cannot block access to Pirate Bay without blocking access to the ISP's which link to it. The only legitimate means available that I can see is in the direct prosecution of piraters themselves, meaning those who rip and distribute such material. Unfortunately, with the advent of modern technology, there is no easy solution to this problem.
The use of strong Digital Rights Management and the vigorous prosecution of all who engage in actions intended to defeat DRM seems to be the most legitimate means, but again with advancing technology, even that becomes difficult when so many people are sufficiently technically proficient and capable of circumventing DRM protection.
It seems to me that the best solution would be one similar to that provided by the Itunes paradigm in which all intellectual property becomes available for download at a reasonably affordable cost. In all probability, to be successful, the record companies and film companies would have to settle for pennies on the dollar profits rather than dollars on the dollar profits.
There would also have to be some sort of perpetuity protection under this paradigm so that, should your computer crash or you buy a new system, you would not lose all of the programming material you had purchased.
Too many times DRM has been the source of immense frustration for those who suffer a disk crash or purchase an entirely new system and lose all of the legally downloaded material. Such occurrences inevitably lead to anger and frustration and piracy of intellectual property.
Ther never will be a perfect system, so the primary question remains, the extent to which you are willing to surrender your access rights to protect your property rights.
BTW This is pure opinion and speculation on my part, I AIN'T NO CONSTUTIONAL LAWYER (but then, I did sleep at a Holiday Inn once

).