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From what I've heard from a few Realtors, is that 580 can be done. Depends on who you're dealing with. Even had a few say with VA the score really didn't matter. Not sure how that works, because we haven't gone through our process as of yet, but they did say this. It appears that these kind of scores, and issues are pushed through when you want a "Quick Move-In" home and you don't have to worry about all the extras. They'll rush things in less than 30 days. Other kind of deals are where all the extra concerns and issues may arise, especially with a 580 score. Just talk to them and they'll tell you if you need to do certain things.
When did the repo occur? Over 12 months ago? If so, and all payments on all of your debts have been paid on time since, then you'd have a chance at a VA mortgage. VA mortgages are more concerned with credit history than credit score, although there are a lot of lenders that will have minimum score requirements for a VA loan (anywhere from 500-620 is where most lenders minimums will come in at).