I think what he means by "carefully presented" is that they need to pick cases where the circumstances can't be cast as "the Dems just want to give illegal immigrants more rights than you have." If you look at the way the Fox Cinematic Universe is presenting the Abrego situation, it goes something like this:
He came into the country "illegally" at some point.
He was arrested for being an MS-13 gang member.
Trump is deporting him because he is an illegal engaged in terrorism in the U.S.
Trump just sent him back to his home country.
Why do you want to protect a terrorist from being sent back to their home country where they can deal with him?
It's all fucking lies, but the average U.S. citizen has no appetite for nuance, so this version of the story is going to resonate with some, especially for those scared of brown immigrants (which is unfortunately a lot). The risk is that if the Dems latch on to a couple of situations like this that can be twisted in the minds of a good chunk of the country, all of a sudden we have another "Russia Russia Russia" situation where, even as the Trump administration engages in more blatant misconduct, people don't bother to listen. Unfortunately, the Dems only have a few chances to make this stick - otherwise people will just tune out.