The short answer is yes, but it depends on your bank. All creditors have the right to pursue the money owed to them, but these days some banks will let the money go, so to speak. If your bank is one of those, then you can "walk away" without having to file bankruptcy. Unfortunately, finding out whether your bank will or will not is not as easy as simply asking them. There really is no way to find out for certain.
You mentioned that you were refused a modification. Banks will only consider a loan mod if the loan modification is packaged and presented in a manner that they accept. Of course, the content is important, e.g. your financial information, the property value, etc., but since banks are literally working on hundreds of thousands of files, they will simply reject a file if it is not structured properly, no matter how valid the contents.
If you can no longer afford the payments and your job prospects are dire, then you absolutely must put the house on the market and find a buyer.