Their embrace of political correctness is the big problem. The left's inability to bash in some skulls and crack down on the illegal immigants/minority activists is the bigger problem.
I do not think you are being honest here. I think that's what you want from the party. The truth is, most voters only insult political correctness when it bugs them. I know a lot of people who love racial jokes, but get huffy about fat jokes because they are overrated, or whatever. The truth is, political correctness is such a non-issue outside of punditland that no election hinges on it. And certainly that's not the Democrats' problem.
Besides, immigration policy and political correctness are only related tangentially. You can call any empathy political correctness if you like. The Democrats shouldn't be cracking down on activists. What in the world? That's free speech. Politically correct as it may be, I'll die to defend that.