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2 things
1. Lenders will almost certainly deny a loan with a cross country move with no jon confirmation. Even if you found a different job, unless it was in the exact same line of work it would probably be a deal killer.
2. Unless you are very familiar with an area or have family/close friends in the area to help, buying a house during a cross country move can be a very bad idea. There is just too strong a chance that you may not like the area/school/job situation/etc or may change your mind and want to move back to where you came from. Probably 1/2 the time people move across country to a unfamiliar area the end up relocating to a different part of that area or moving back to where they come from within a few years. Not to say this is your case at all, but something to think about.