In this particular case 'sick' is being replaced by 'gay'...which casts an allusion I personally don't think is necessarily positive but whatever.
Concept of this, despite my tagging this as being a holiday it's more of a protest sorta deal, is to show the American public how essential gays are to the work force. Actually it's part of this that may cause an issue given that the economy being in the crappy state it is, several gays that have been interviewed say they'll be unable to call in gay because they can't afford to.
They'll be supporting this movement in other ways.
While I don't have a full handle on this, clearly, I'm calling in gay too. Granted, I'm not gay and I'm currently unemployed but it's the thought that counts.