Today, my American room mate was trying to tell me something and I had to ask him to repeat it three times until I guessed what his question was. It turns out he was saying "did I tell you what happened to him?" and he was pronouncing the first part really strangely. It was like "day tell you what happened to him?". Is this really how American say "Did I"?
Edit: He is from California
Remember, there's no single American accent. Different Americans will say things somewhat differently, depending on what dialects they were exposed to when. My own accent still has a lot of New York in it but has been sliding toward Bostonian. My brother's picked up a bit of Northern Californian and Wisconsin influence in his speech.
However: Yes, I've occasionally heard a version "did I" which sounded something like "dye". You can think of that as dropping the first syllable -- "'d I tell you...?" -- which would make it related to "what'd" as a contraction of "what did".
Informal spoken forms of a language often elide (drop), weaken, or slide through sounds which technically should be there but which are awkward to pronounce or which aren't completely necessary for comprehensibility. In fact, one of the things that makes a non-native speaker recognizable is that they usually follow the formal rules more strictly than someone who grew up with the language would. The hard thing is learning the unwritten rules for which "cheats" one can get away with -- and as I said in the first paragraph, that varies from place to place.
And often it happens entirely unconsciously. When I was learning Spanish, I found that there were several pronunciations which folks used when speaking at a normal speed rather than word-by-word -- but if asked, they would strenuously deny that this was what they had actually said.
So: Yes, some Americans sometimes say it something like that. Not all, not all the time, and they may not be aware they're doing it.
