I suspect this is part of the problem. Just make vague demands and let people insert their own interpretations. I don't think that many really came here wanting citizenship or they would have gone about it differently. (However, I also think many changed their mind later.) My impression is that they mainly want to work so they can send the money back home or save it and go back later. Much like some people go to work in Saudi Arabia or the Alaskan pipeline, for example, get paid more than they would otherwise for a few years then come back.
The illegals that I've met just want to work; perhaps become citizens one day if they are really lucky. After all, the US is, as they say, the big PX. Many of them manage, after they've been here awhile, to acquire their green cards. As poor as they are, many of them consider their lives here better than anything they could have hoped for at home. I think their perception is that they'd never have had the chance to work and live here if they went through legal channels. Too many obstructions on both ends, their country's and ours.