Getting your certificate of eligibility shouldn't take long at all. If you are currently on active duty you must show evidence of how long you have left on active duty, typically, just a copy of your orders is all it takes. The easiest way to get it is to meet with a broker who is registered with the VA. Take a copy of your orders, or your DD-214 if you are no longer on active duty, and they can get a certificate ordered online that only takes a few days. You will have to fill out the same form as well for when it is submitted to the lender.
Also, recently I have found that a lot of veterans are being told that they have to have higher credit scores in order for them to use their VA benefits. That is misleading. Some of the more popular lenders require a higher credit score but there are hundreds of lenders to choose from. A broker or direct lender may try to get you to do a different type of loan if you have bad credit. DO NOT ACCEPT IT! Your VA Loan benefits WILL SAVE YOU A LOT OF MONEY! Instead of having to pay for Mortgage Insurance, the VA requires a 2% funding fee which can be rolled into the loan. MI on a $100,000 loan will cost you ~$65 a month until you reach 80% Loan-to-Value on your home. The VA loan will have a slightly higher rate,~.5%, which will result in only about $30 a month.
Sorry for rambling on there. I'm in Nashville but I think a buddy of mine has a license in NC to help you out with it.