I don't know what your political leanings are, but this is pretty much the way I feel when the Left tells white people (e.g. me) they need to pay reparations 150+ years later.
So yes, that kind of attitude is sad and being blamed for something that was no fault of yours does suck.
With due respect, I think you're missing a very important difference here...
I presume you're referring to affirmative action, or other policy measures that promote or otherwise advantage underrepresented groups? If so, that's the key difference; underrepresentation amounts to inequality of opportunity. Although I may not have personally discriminated against members of an underrepresented group, the fact remains that those individuals face much greater barriers to earning the life they desire -- and the corollary is also true, that I have enjoyed a socio-economic advantage simply by virtue of being born a heterosexual white male in North America.
Did I do anything to deserve that advantage? No. Did I do anything to deserve being disadvantaged? No. But can I do something, right now, to correct for the systemic discrimination that I'm implicit in? Yes. Affirmative action is a temporary measure to even the playing field, so to speak, and when everyone has a fair shake (i.e., equality of opportunity), then we all benefit from living in a more just and equal society. You can't move forward collectively if you leave some behind; progress is necessarily slow.
With DACA, these individuals are not receiving a free ride at your expense, but the opportunity to earn a living and contribute to the country that has given them safe harbour, so to speak. If these individuals betray that opportunity through crime or other means, they still face deportation. Instead of viewing DACA as a personal punishment, view it as a personal and collective sacrifice for a better and more just society/country.
The thought that immigration necessarily erodes culture or economic prosperity is self-evidently false; borne out of fear, not evidence.
No one should be surprised by this sort of resistance, though. It's difficult to acknowledge when you have received undeserved advantage, and it's even more difficult to willingly accede it. My views have changed over time, and I trust others' will too -- with time, and more importantly, education. Labelling and vilifying the "left" or "right" accomplishes nothing; this isn't team sports, and everyone is in it together.