My guess would be Yes on both parts. There is also another option. They wish to have more power and control and the 2nd amendment stands in their way. I think that more than a few have this third option at heart.
People who oppose punishing criminals support trying to make the world safe by hiding all the dangerous hardware. So who opposes punishing criminals? One group is criminal defense lawyers. Because they make a living defending criminals, they often have a cognitive dissonance that is solved by concluding that there are better ways to make society safe than locking up their client. Gun control is one of those ways. Criminal defense attorneys are usually members of the Trial Lawyers' Association - a very powerful lobby group. I suspect that the Trial Lawyers lobby for gun control.