The pro illegal alien lobby was gop policy from 1980 through 2008, and I voted for a few gopers, LOL I worked with illegal aliens too.
But I agree with you so far as no violent felony (and that includes DUI), we could just give them a green card. Personally, I wouldn't give them soc sec eligibiltiy, but they pay the payroll taxes, and no Obamacare eligibility either. Not to be an asshole, but when they came here, that was not part of the nod and a wink deal we offered to ignore illegal immigration.
I doubt the dems would give that much, but I would happily, in exchange for serious fines on employers and a vigorous catch and pitch back over the border for all immigrants without legal status, including amnesty seekers.