That is a personal decision based on income and expenses. Check out a mortgage calculator at www.bankrate.com to get an idea of what your financing options are. You may be in a position to buy another property and then rent, foreclose or short sale the property you live in. That option will depend on your new lender, current credit and income. If this is an option you want to explore, you will want to hold off on doing any modification to your current loan because a future lender may require you wait 3 years from the time of the modification before you can qualify for a new loan. Even if you were never late.
I have been pondering how to answer your question the last 45 minutes. First, in general, I feel a 30 year fixed is better than a 15, even with the slightly lower rate, as you can always pay at the 15 year rate, but, if faced with hard times, you can back off to the 30 year rate. This is what my wife and I have done with our own home, and, when we hit the downturn, we were able to back off the higher payments without being in default.
As to the priority of getting out of the home ASAP, waiting to refinance is contrary to that goal, and it is financially wasteful. You will need to short sell, and, with very few exceptions, a short sale has a 2 year "waiting period" before you can get a new conventional loan. So, in order to move as soon as possible, other options need to be discussed. What I will share with you is that your credit is not at all ruined if you take action today, contrary to what many others may have told you. It is worthwhile to meet with an attorney to discuss all of your options, if for no other reason than to ensure that whatever final decision you make, you know you've made it with accurate, unbiased information.
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The part of your question about whether to accept loan terms is really more of a financial question than a legal question. Many times if you do the analysis of the value of your credit, you find that the enormous price of paying off an "underwater" house is simply not worth it.
What I would do if I were you is consult with an attorney who is familiar with the HARP program. Most attorneys, including me and even many real estate attorneys, do not know much about the HARP program. Bert Millett is one attorney who does. His phone number is 480-655-7440 if you care to follow up. Good luck.
This answer does not constitute legal advice. I am admitted in the State of Arizona only. This advice is based on general principles of law that may or may not relate to your specific situation. Facts and laws change and these possible changes will affect the advice provided here. You should not rely on this advice alone, and nothing in these communications creates an attorney-client relationship.