Please carefully consult your purchase contract. In most cases realtors will stipulate language that includes prepaids in the seller concessions. At the same time if the contract simply stipulates $10k in closing costs without the language of prepaids, you won't be able to apply them in this way.
I'm stretching my brain to try and figure out why there would be $8k in pure closing costs. Either you are buying down the rate and paying the fees to offset the compensation the broker is losing in the rate pricing, or you are being overcharged, that is unless the loan amount is over $500k.
My suggestion is that you contact a friend you trust and ask them who they have used as a mortgage provider. Contact this individual and go over all your paperwork with them. It sounds to me like you might uncover some charges and fees you won't be comfortable with.
12K for closing costs seems abnormally high to me. Are you buying the rate down? What is the loan amount? It sounds like you are working with a broker. Additionally, if you are doing an FHA loan you can get those most places for less in cost. To answer your question: whatever difference it does't cover you will have to as a consumer. The 10 k concessions can be used for prepaids as long as it is written in the contract. Some of your pre-paids may be asorbed by a tax credit you will recieve depending on when you close. But if your only getting concessions of 10K and prepaids and closing costs are 12K, you will have to make up the difference out of pocket. Finally, I would shop around for mortgages and loan officers. I would never pay 8K in closing costs on any purchase. So if it's not too late I would look around and a second opinion for sure. Hope this helps! Call me if you have futher questions.