The Free Speech Coalition has released an excellent analysis of the constitutionality of grassroots lobbying disclosure. It can be found here: LINK
Here are some additional references…
-CCP’s analysis of constitutional protection for anonymous speech: LINK
-CCP’s original Policy Primer on grassroots lobbying disclosure: LINK
-CCP Exec. Director Steve Hoersting’s op-ed on one of the most famous exponents of grassroots lobbying: LINK
-CCP Chairman Brad Smith’s blog post on one of the most infamous exponents of disclosure: LINK