If you only heard the word, what was the pronunciation? As a prefix, semi- can be pronounced either similar to German or with a long English I, but as a word standing alone, it's usually (in AE) the latter, so it would rhyme with, say, 'them eyes.'
I think that's why dude thought of 'vice,' because it has the same vowel sound, and that seems like a reasonable guess to me too.
Another idea might be ICE (Immigration & Customs Enforcement, something like that), pronounced 'ice' (which is also slang for 'kill' -- an evil Orwellian concept for which we have the Bush administration to thank). They would certainly frighten someone who was an illegal immigrant, because they would probably deport her.
Or perhaps 'police with semis,' that is, guns, semiautomatic rifles?
Or, last thought, something with 'guys,' like 'bad guys'? 'Some guys'? 'Them guys'?
I think we can rule out the other guesses so far. We don't actually use 'semi-military' to mean a paramilitary in the countable sense of a fighter, as far as I know, and we don't use 'semi' as a short form for semi-military or semi-official. And there are no paramilitary forces in US cities anyway, that would be the Colombian jungle or somewhere else.
There are other forces that might seem as threatening as police -- security guards, ATF, Mafia, criminal gangs -- but none with a similar sound that I can think of.