The short answer: He might be right, sort of, and “it depends.”
No one is compelled to support an enterprise to which they object. Boycotts of merchants or vendors (or, presumably, entertainers), by groups of like-minded people are quite legal.
However, there are laws to prevent coercion in arranging a boycott.
Thus, if the GLBT community announced, en masse, that they will not watch his show, (and they encouraged others who support GLBT rights to also boycott the show), they are perfectly within their rights to do so. If enough people choose to not watch, the sponsors will lose interest, and the show will go unfunded.
However, if a group exerts undue influence on the sponsors to withdraw funding, then Savage can claim that is is restraint of trade, rather than simply like-minded individuals protesting with a boycott.
This point gets tricky, however, as it is unlikely that the GLBT community sent around a couple of guys with guns to order the sponsors to withdraw support. At that point, the question becomes one of “What is coercion?” (which is why he is threatening a lawsuit and not threatening to go to the Attorney General to press charges). Over the years, many advertisers have withdrawn support for shows on the presumption that their support of a show will offend potential customers. Last year, a whole slew of sponsors pulled out of Bill Maher’s Politically Incorrect, despite the fact that his ratings never dropped. However, they were simply letting their PR departments run in fear of a potential backlash, and there was no suggestion of coercion–although cowardice was indicated. Several years ago, GM pulled out of sponsoring a TV movier on the life of Jesus based on the rumblings among some Southern Baptists–who had no idea what was really going to be shown–but, again, there was no suggestion of coerciaon, simply a PR department running scared. Savage wants to claim–and if he goes to court, will need to demonstrate–that there is some sort of deliberate, undue, and illegal pressure brought by the GLBT and women’s rights groups that compelled his sponsors to withdraw when then they would not normally have done so.
(Of course, making a big deal of this is a convenient way for Savage to get more publicity for his show, but it would be cynical, (cynical, I say), to suggest that he is raising this ruckus in order to drum up free advertsing.)