I come from a very large extended family where the vast majority of folks are very conservative, which means political conversations end up with me being ganged up on. The election of 2000 pretty much ruined Thanksgiving that year because the topic kept coming up in conversation, and I kept getting into fights about it. After that I learned two tactics that have led to more peace and enjoyable holidays. Perhaps they can help you, too.
Tactic #1: Pacifism
This is the stance I tend to use the most. There is actually an informal truce between my parents and I when it comes to talking about politics, but my other relatives are not as mindful. When they start bringing this stuff up I usually first tell them "I don't want to talk about it." If that doesn't work, I say "I disagree with you, but I'd rather not get into it." In the very rare cases where that does not bring an end to it, I just get up and leave the room. It can be very difficult to take this course, since it means holding one's tongue in the face of outrageous or even offensive statements, Over the years I've learned I can't change their minds, that they take any political arguments personally, and that deep down we love each other and just want to have a pleasant time together. Why destroy that trying to reason with someone who spews Fox News talking points?
Tactic #2: Massive Retaliation
Sometimes I resort to this tactic, usually when someone brings up something political apropos of nothing, and in a way that is offensive or a personal affront. For example, one of my cousins responded to the use of racial slurs by one of our uncles by yelling at him to knock it off and never use those words in front of her children again. (It actually worked!) This summer another uncle was goading me about how great Chris Christie is, and after refusing to relent when I tried to change the subject, I just unloaded about how insensitive he was to the fact that my wife is a New Jersey teacher and that he has been scapegoating people like her with his blustering rhetoric and that his policies had actually taken money out of my family's pockets. He was pretty taken aback at my passion, and just dropped it. This tactic doesn't work well with things like the Affordable Care Act, but sometimes is necessary when confronted by birthers, Christian dominionists, or Trayvon haters. You shouldn't even have to listen to that kind of bullshit.