While a lawsuit for $13,000 might be unlikely now, the time share company certainly has the ability to turn the account over to a Canadian collection agency and get the default on your credit reports.
Worse, your debt doesn't stop at the $13,000. It keeps growing with interest, late fees, annual fees and, eventually, attorney fees. When the debt gets big enough it could very well make a lawsuit worthwhile.
So, no, you don't get to just "walk away." At least not without potentially serious financial consequences.
I suggest you address your problem by googling "selling a time share" or "getting out of a time share."
There are helpful resources all over the internet.

