Well, they’re all pounding Trump as hard as they can. No question about that. Presumably they’re afraid of him. They accuse Cruz of being an extremist, but don’t beat on him nearly as hard.
The Natural Born citizen question is arguable. It’s possible that they want to push Cruz over Trump, and then eliminate him by lawsuit after he is nominated. Since Justice Roberts seems to be subject to blackmail, they may feel that they have a lock on the Supreme Court on that issue.
I have no doubt that the dems will do everything and anything they can to win.