I heard Rush say that it takes the average illegal immigrant 45 days to reach our border from their origin.
Ebola has an incubation period of at most 21 days. In most cases, it is closer to 8 days.
Even with someone who has a very long incubation before symptoms appear, there is little chance of them still being alive once they reach our border.
While Ebola could get here by plane, it is highly unlikely to get here via illegal immigrants. The other diseases, however, are a concern.
What you are missing is that illegals generally travel in groups, and meet up with other groups along the way. Disease does not have to travel all the way here in one host, it can be relayed. The sick person will infect at least some of the other people encountered. If an illegal becomes very ill, they try even harder to get here for medical treatment- meaning they would be unlikely to stop their travel until their illness forces them to stop.