Actually, I think it is possible.
Strangely enough I was considering it a bit more earlier, it's kind of a fun challenge to try to think of ways of making this feasible. Ultimately, though, I can't see it as anything more than a flight of fancy.
A minimum of three rest days would be necessary, and four wouldn't be out of the question. If you started on the Saturday and had five stages in the US, then two rest days for the transfer. A short time-trial on the following Saturday (less than 10km), a 60km sprinters' stage Sunday then another rest day on Monday to allow one more readjustment to the time zone. Then carry on as normal, with one more rest day to break up what would otherwise be 13 consecutive stages. Another suggestion might be to make it a one-off two-and-a-half week race as opposed to three weeks, starting on a Wednesday. As above, but without the fourth rest day.
It does all sound ridiculous and would probably end up being the worst Giro ever, but on the understanding that it would be a complete one-off I wouldn't be against trying it. My only worry, as dimspace suggests, would be the idea catching on and spreading. Whoever gets there first gets to do it once, I say, just so that we can have it confirmed that it really is as utterly stupid as it seems. After that it's consigned to the history books.
Another issue is that it would frankly look a little bit desperate (no, very
desperate) on the part of RCS, as though they are really worried about the Giro being surpassed by California and want to do something zany to remind everyone they're there, which is totally unnecessary. Zoncolan, the Finestre and Plan de Corones are crazy enough for most people, I think.
Speaking of the Finestre... when's that coming back?