The old "left" of Carter and Bill Clinton are no longer driving the agenda of the Dems today...the progressives are. Bill Clinton said he was very much against illegal immigration in the mid-90s. The progressive left desires much bigger government control, more social programs (which require higher taxes), etc. And when studies show that immigrants, specifically those from Mexico and Latin America, are much more likely to support an increase in government funded social programs...well, there you go. And the tradional GOP doesn't want to stop illegal immigrantion outright because that goes against cheaper labor. So here we are. And who loses: The middle class taxpayer, lower income Americans who work in construction, Americans who live in areas that have seen an increased amount of gang activity made up of illegal immigrants, etc.
It's sad...but when you hate what America has mostly been over the last few decades and believe it needs fixing (ACA, public option, higher taxes, etc), then this is how you see the "change".