Do you have a construction loan on this property? Or does the builder? If you hold a construction loan, does it convert to a permanent loan?
If you have a purchase contract, does it have a mortgage contingency clause? Look for that clause in your contract. Did an attorney or Realtor help you with the contract at the time of purchase?
Stretching income to qualify is not a good idea. You do not want to make any misrepresentations on your loan app, or venture in to an area that may be considered fraudulent. You also do not want to get into a loan that you cannot repay.
It is possible for the builder to pay closing costs on your behalf. If the builder paid closing costs based upon an existing contract price, would it make a substantial enough difference in the monthly payment to make it affordable for you? Your lender would have to know about this. The builder cannot pay closing costs without full disclosure to the lender. An increase to an existing contract to cover closing costs would be a modification to the contract that you should not do without consulting an attorney, particularly if there is a loan application made based upon a submitted contract.
If you are in breach of a contract, the other party to the contract might sue for specific performance or damages if you fail to perform. You can also negotiate a settlement if you are in breach of a contract. I am not implying you are or are not in breach. I am not an attorney, nor do I have the details of your agreement. You need an attorney to review the contract terms and determine your rights and obligations and give you legal and accurate advice.
So sorry to read about your dilemma.
What you need is a GOOD attorney who handles real estate to help advise you of your rights and possible solutions to this matter. You can't afford to pay the builder and the builder can't get blood from a stone.
Unless there is a attorney here on Trulia, this is not something we real estate agents are qualified to advise on.
However, I was thinking that if you still have a place to live now, the builder can possibly sell the unfinished home to someone else, and finish it for them, taking you off the hook. Is that an option?