I have yet to see a "gun grabber" that is not a statist. They know they are helpless and weak, unable to fight the battle themselves, so they attempt to play on what they perceive as our weakness; namely, that we obey the law. Thus, laws defining this and that as forbidden will do for them what they cannot do themselves: make us helpless, just like them.
I have known ones that are both conservatives and statists. That is, they think that they can keep power semi-permanently and that they need to be the hub of power. They no more trust the masses than do liberals and in so doing are happy to use the law to keep those masses from having hard power.
Remember, Fascists take guns just as fast as Communists...
That being said, conservatives are more comfortable with guns than liberals in my experience. So I assume that, as a trend, they are less likely to grab. But at the same time, I don't assume...