One big problem with the idea that teachers ought to be personally drawing some kind of line in the sand over the Common Core is that the entire notion of what standards are and how they are to be used is so vaguely defined. It is like gearing up to protest the passage of a new law in a country with no constitution or functioning judiciary or even police force.
For example, one group of people are all wound up about the importance of the fidelity of implementation of the standards, but if you'd ask them, say, why literature standard six for grade 9-10 ("Analyze a particular point of view or cultural experience reflected in a work of literature from outside the United States...") does not apply to literature from inside the United States, they'd have no interest in answering the question, aside from possibly pointing out that I'm not supposed to read the standard so literally. Which is fine, but can I ignore the words I find inconvenient too?
The Common Core just isn't that different than what it replaces, and frankly it isn't worse than some of the other existing standards, and in the past teachers have readily ignored the impractical parts of academic standards with no bad results for themselves or their students.
The implementation is the catch, as always, and in particular, the tests are what will deserve a higher level of scrutiny and, let's be frank, internet-scale leaks of content, than any test has before.