Might be very close, but the good credit score is going to help. The low car payment (I assume that is monthly) and very small student loan are also in your favor. There are lenders that will still let you do as little as 5% down, but to get the best rates avoid PMI you really should should for 20% down. The other option is to do the math on a 5/15/80 deal, where you use an initial second to avoid PMI -- you might have a good score to not get a terrible rate on the second. If you could get to 10/10/80 with your score you should be in good shape with several lenders...
Are you first time buyers? If so there may be lenders willing to "front" you the refund amount -- I generally discourage that sort of think, but it may be an option to pursue, so long as you get the DETAILS on how they are fronting that money...
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