Are we talking about illegal immigrants voting? How often do you think that happens, percentage-wise? Just curious.
Los Angeles Times poll of registered voters has 41% of California Latinos admitting to being born in a different country. These results are quite stable from poll to poll. It's within the realm of possibility that they're just confused but then you'd have news stories every election about millions of illegal immigrants being turned away at the California polls. Saying they must've come through legal channels just insults our intelligence.
Edit: Also, a common Democratic "voter suppression" complaint is that Republicans supposedly make Spanish-language robocalls saying that illegal immigrants are subject to deportation if they vote. This is, of course, an implicit admission that illegal immigrants do vote. If such a thing actually is occuring, it also indicates that Republicans consider it a genuine concern and it isn't just something they made up.
Thing is, in some mid 20th century sweeps to gather up illegal Mexican immigrants and deport them back to Mexico, we ended up deporting people who actually were U.S. citizens. So it's not at all unreasonable that if such robocalls were considered believable that some people legally here would be worried they would get sent to Mexico nonetheless because it has happened before.