[0]: https://en.wikipedia.org/wiki/1994_California_Proposition_18...
For example, a 9% swing results in a tie.
Sure, having benefits is nice, but most illegal immigrants aren't coming to the US for the benefits, so if their options are "less are allowed, but the ones that are allowed get benefits", and "more are allowed, but no benefits", almost all non-Americans would chose the second (because America even without benefits would be a massive increase in their quality of life [0]).
[0] - Or it wouldn't be a increase in quality of life, in which they wouldn't come either way. I just have a hard time thinking of many people (compared to the size of the "always better" and "always worse" groups) whose quality of life in America without benefits would be worse relative to their home country, but better than their home country if given benefits (those that are normally given to Americans) in America.