Clinton Signing Statement
Here's an interesting example of a presidential signing statement that declines to enforce part of the law in question. It's from President Clinton, on signing the Telecommunications Act of 1996:
I do object to the provision in the Act concerning the transmittal of abortion-related speech and information. Current law, 18 U.S.C. 1462, prohibits transmittal of this information by certain means, and the Act would extend that law to cover transmittal by interactive computer services. The Department of Justice has advised me of its long-standing policy that this and related abortion provisions in current law are unconstitutional and will not be enforced because they violate the First Amendment. The Department has reviewed this provision of S. 652 and advises me that it provides no basis for altering that policy. Therefore, the Department will continue to decline to enforce that provision of current law, amended by this legislation, as applied to abortion-related speech.