The standard recommendation for connecting flights after your first flight arriving in the US is to allow 2 1/2 hours. See, e.g. the Washington Post article "What to expect when connecting from an international flight" and it's comments (don't think I can put a link here).
But I see above recommendations for 4 hours. Is the process really that much longer for someone coming in on a K-1 visa like my fiancee will? She says she's heard, and one poster above agrees, they just ask a few questions.