The fact that he calls himself a conservative and yet feels left behind by 'his' party that has run off the rails pandering to a few key demographics is part of the drama.
The problem is that it's really poorly presented on the show because, based off of what we've seen, Will is not really a conservative. On almost every issue that the show has addressed, from gay marriage to gun control, from social security to free-market economics, Will has not expressed traditional conservative points of view. The sole conservative value he was shown to hold is that he's pro-life, and that was a single line thrown out there in an episode about an entirely different subject. In the same episode he revealed that the reason he is a Republican is that he grew up in a rural area where everyone is a Republican and that's all he knew. I hate the overuse of the RINO label as much as anyone, but Will really does come across as a Republican in name only.
Let's be honest here, the reason why Will is a Republican is that Aaron Sorkin wanted to go after the Tea Party and he felt that having the main character be a Republican would act as a shield from the potential criticism of the show's liberal leanings. But he did a really poor job of portraying Will as a conservative, it's one of the leading criticisms of the show, and it's a good sign that Sorkin is trying to address that in season 2.