Moderate Republicans and Conservative Democrats?

Here is something that I don't quite understand. How does one define their political association? And once you do so, what do you do when your chosen party morphes into something that you no longer believe in?

Democrats are quite used to their party becoming more moderate than the liberal grassroots activist. Now the Republicans are seeing their party veer sharply to the right (and right off a cliff, if you ask me). So, where does the self-defined moderate Republican pledge his allegiance? And when can a conservative Southern Democrat just admit that he/she is a Republican?

And if this Republican fiscal insanity continues, where will the fiscal conservatives of the world turn? It seems that the Democrats are becoming the budget hawks. The Emperor's foreign wars are adding up and his domestic tax cuts make less sense each passing day.