The problem is that the average person bot agrees that only the worst of the worst should go, but also believes that there are far, far, far more of such people out there than actually exist. This is why we see poll metrics saying things like a majority of people agree with the deportations but disagree with how it is being done.
Ah but that was a sleight of hand! They're doing exactly what they said they'd do.
They said they'd target violent criminals, but they didn't say they wouldn't target non violent criminals as well. People who heard that were wishcasting.
Whether or not they are a "priority" is semantics. If you hear them explain it, they're all defacto criminals for being undocumented, and therefore equally culpable as a murder or a rapist in matters of deportation.
The crime they're concerned about over all others is illegal immigration. According to them, an illegal immigrant who has done nothing else wrong deserves to be deported just as much as rapist illegal immigrant.
They've stated themselves that they don't have the resources for due process in all of these cases. So, yes. That is precisely what they should do. They can stop putting effort and resources into pointless ones and actually do their job.
So now they have not only to determine a person is an illegal alien; on top of that, you want them to somehow determine who is "heinous" and who is "good"? It seems a lot more work, considering the fact that there's no objective scale for "being heinous" (what do you do? You ask their friends?) but there's a reasonably objective way of telling if a person is illegaly residing in US or not.
There is a pretty reasonable way to determine if someone is "heinous" or not, committing a violent crime and being found guilty of it. And if going through a criminal justice system is "too much work", then I'm got news for you about who that's going to be applying to next...
So, you know, maybe they could try to do what they said they'd do for once?