There doesn't seem to have been much of a lobbying process. It was accepted with little debate, and other options to promote progress were rejected. Copyright was a well-established practice inherited from British common law, and viewed by Madison to be clearly in the public interest:
"The utility of this power will scarcely be questioned. The copyright of authors has been solemnly adjudged in Great Britain, to be a right of common law. The right to useful inventions seems with equal reason to belong to the inventors. The public good fully coincides in both cases with the claims of individuals. The States cannot separately make effectual provisions for either of the cases, and most of them have anticipated the decision of this point, by laws passed at the instance of Congress." Federalist 43
For more background: http://www.copyhype.com/2010/09/copyright-and-the-constituti...
