There you get to extremes on both sides.
Republicans have very well known extremists who are tied directly to the party, but the Democratic extremists tend to but unlinked to the party itself.
Still in either case when an extremist talks, they generate discussion amongst the moderates and people then try and figure out where they stand and make some decisions.
In the illegal immigration debate, you've got some people who just plain don't want any immigrants and others who if you let them would throw the borders wide open. but more in the middle is topics like 'Well we need some control over it' or 'We really should make sure people are learning our language' etc... which are moderate and practical points.
Someone screaming out 'You Lie' at a specific point did draw attention to that point - And while you've got some extremism at both ends, the result kind of brings the general populace in. Bringing a little attention on this one probably makes most people say "Oh, you're right, I don't want illegal immigrants to be allowed to buy it" and then the Dems have to decide if that's a hill they feel like dying on.
The economic issues are hard enough to dispute because no one can actually say what will happen, only what they think might be the impact since there's no way to accurately know what it will do. It might cause unfair competition, it might not, it might raises costs, it might lower them. No one really know, they're just trying to do what they think would work.
But questions like the immigration issue are actual 'ought to' issues as opposed to 'how to' issues. It's easier to say 'I don't think illegl immigrants ought to be allowed to buy it' because that's more a political and philosophical question...the question of 'Will illegal immigrant's participation financially harm the plan?' is more a matter of debate.
Again you can generalize this to all issues, and its why it was probably effective this time...you've got tons of potential discussion points on a bill which contain murkiness and economics and so forth, but there's a few points that are just 'Ought to' issues. And if you think you're probably in the majority on the ought to issue, and you snap attention to that point, you'll probably win that point even when it would have been otherwise lost in the shuffle.
the way I parse this term is that what an illegal immigrant does is illegal.
I'm not sure why you'd parse it that way. To me that reads as if their immigration is..And continues to be...illegal. So it does indeed reflect on their continued status. That doesn't imply their other actions are illegal to me, but it does properly denote that they have engaged in and continue to engage in an illegal activity.
Their existance isn't against the law...but their presence is.
Undocumented is actually imprecise, you may in fact be documented and still be there illegally, it doesn't make any reference to illegal action.
If you break into a house and then don't steal anything and hangout there, you're still committing a crime perpetually.