Voter Fraud: How Many Illegal Immigrants Are Voting in US Elections?

At dinner last night, one of my dining companions suggested–and everyone at the table seemed to agree–that the United States has a serious voter fraud problem. Illegal immigrants, he claimed, were voting in such large numbers as to potentially skew the results of many elections. Everyone else at the table seemed to accept this as widely-known. 

I was disbelieving: Outright voter fraud on that scale, and I’d never heard of it? They seemed to think I was naive and out of touch for doubting it. 

Is it true? If it is, why aren’t people angrier about it? I scream my head off about the possibility of voter fraud in Turkey. Should I be screaming my head off about this, too?

Voter fraud is serious. If this is happening, it should be much bigger news, no?