Gov. Palin uses the rhetoric of the "First Amendment" in a way that's not uncommon (see here if the download from the other location doesn't work), but that I think is quite mistaken:
[Q, host Chris Plante:] ... Is the news media doing its job? Are you getting a fair shake, the Republicans getting a fair shake, this year?
[Palin:] I don't think they are doing their job when they suggest that calling the candidate out on their record, their plans for this country, and their associations is mean-spirited, or negative campaigning. If they convince enough voters that that is negative campaigning for me to call Barack Obama out on his associations, then I don't know what the future of our country would be in terms of First Amendment rights and our ability to ask questions without fear of attacks by the mainstream media. Look at Joe the Plumber, good old Joe the Plumber in Toledo, Ohio, he just asked a simple, straightforward question, and the media started investigating and attacking him. So, you know, there is some fear there, and in those terms, no, I don't think that they've been doing their job in that kind of context.
I recognize that legal terms such as "First Amendment rights" are sometimes used loosely, including to refer to freedom from private retaliation against speakers. (The First Amendment itself applies only to government action, either directly or via the Fourteenth Amendment.) And sometimes this loose usage might not much interfere with the force of the argument, for instance, if someone complains about a private college's violating its students' First Amendments by expelling them for their speech.
But here the looser usage just doesn't make much sense. The media is "attack[ing]" Palin simply by exercising its own First Amendment rights to criticize Palin's statements. Likewise, Palin herself is exercising her First Amendment rights in criticizing Sen. Obama's exercise of his First Amendment right to freedom of political association (and just as critics of Obama's links with Rev. Wright criticized Obama's exercise of his First Amendment right to freedom of religious and political association). If the media's "attack[s]" on Palin jeopardize "our First Amendment rights," then Palin's criticism of Obama equally jeopardize his First Amendment rights.
The better view, I think, is that our First Amendment rights aren't much at issue in this discussion. Obama is exercising his First Amendment rights, Palin is exercising hers, the media is exercising its, and no-one's First Amendment rights are in jeopardy. If Palin wants to argue that her statements are being mislabeled as negative campaigning or as mean-spirited, or that negative campaigning is being improperly maligned (a view that I generally take myself), that's fine. But that requires a substantive defense, not just an appeal to First Amendment rights.
Thanks to Victor Steinbok for the pointer.