You don't need to declare bankruptcy but you will get a ding on your credit if you walk. Confirm your deed is in Florida. If so, Florida is a non-judicial, anti-deficiency state if you don't object to the foreclosure for Westgate to take back your timeshare. If you object, or are perceived to object (be careful they may try to trap you or a family member who answers the phone into objecting), then you lose your rights and they can go after other assets you may have. So do absolutely nothing. Do not respond. Do not give them more money. Ignore the calls and letters from debt collectors and take the credit hit if that is your only option.
Check out the state timeshare laws in the sticky for Florida below, and pay for an hour with a real estate attorney in Florida with this information to confirm your options because we are not lawyers.
Florida – FL, inaction or non-objection results in estate, anti-deficiency foreclosure, but objection leads to judicial, deficiency action: http://www.leg.state.fl.us/Statutes/index.cfm?App_mode=Display_Statute&URL=0700-0799/0721/0721.html
If you do pursue this option, please report back to TUG what happened to your credit so you can pay it forward to others.
How much do you have left on the loan? If it is small enough it might be easier to pursue what others suggested above.