I was so curious about that statement, as it seemed counterintuitive as something Obama would actually say. (Fwiw, if that were an actual quote, look at the difference a comma would make: "Don't worry, if you're eligible, just go vote").
Anyway, I found this entry at Snopes that seems to pertain to this claim.
https://www.snopes.com/fact-check/obama-encouraged-illegal-aliens-to-vote/
From the entry: "In the full interview, it’s clear Obama is urging Latino citizens to vote in order to give voice to members of their community who are precluded from doing so by lack of citizenship, not urging non-citizens to vote illegally. Rodriguez’s question seems to be addressing a fear that voting will result in scrutiny on one’s family which could result in deportation of undocumented relatives".
The relevant part of the interview is at the link to judge, including this exchange:
RODRIGUEZ: This has been a huge fear presented especially during this election.
OBAMA: And the reason that fear is promoted is because they don’t want people voting. People are discouraged from voting and part of what is important for Latino citizens is to make your voice heard, because you’re not just speaking for yourself. You’re speaking for family members, friends, classmates of yours in school…
RODRIGUEZ: Your entire community.
OBAMA: … who may not have a voice. Who can’t legally vote. But they’re counting on you to make sure that you have the courage to make your voice heard.
Thanks for this contribution. I'm sure there are all kinds of fears playing upon folks on every side of this question.
But it is a racist or race=mongering statement on Obama's part to infer that one Latino can vote for those who can't, representing a sort of homogenous community perception. It is a noxious claim that we could rely on such representation of incoming folks. Trump has been getting more Latino and black votes than former Republican candidates, partly because he talks about jobs and helping businesses here, despite--or like-- my probably equally invalid generalization that lots of the Latino newcomers have been schooled in slavish obedience to authorities they have absolutely no hope of doing anything at all for them.
The cocky sort of claims dems make on segmented portions of the electorate is falling short, I believe. Socialism is not what people come here for. They want a chance to work and build a better life.
I'll take the notes you've brought here as an alert that Obama is actually pretty clever, and whether an open borders believer or not, he's not going to just run his mouth like that.
Well, I've advertised my concerns and motives to get facts, now lets see what is really going on.