Hmm I think you confuse the natural / granted rights concepts. Natural rights and God-given rights are synonymous - they are rights that are consistent with the nature of mankind. Things that man has the power to do, absent an external force imposed upon him/her by another, merely by the faculties and capacities of mind and body are natural rights. Speech, thought, worship, defense, movement, and so on. Property rights are also sometimes lumped into natural rights, as he or she that produces something has the greatest right to the product, and having the greatest right confers the power to control or consume the product.
The drafters of the US Constitution were adherents of natural rights, particularly Jefferson and Madison, and the Declaration of Independence and the Constitution itself incorporate the notions of natural/god-given rights within those documents.
Granted rights are those non-natural rights that are enacted into law or provided by private contract and agreement. Progressives often confuse natural rights with Constitutional rights - implying that rights to self-defense, speech, movement, etc., only exist through enactment of law. The Constitution expressly repudiates this viewpoint, however.
To your second point, Rush like most political commentators has no understanding of natural v. legal rights. Judge Napolitano has by far the best command of natural and legal rights theory, and their relationship to American Constitution and Law.
I don't have a tube, but maybe one of you do. 
