Hello Carissa. No, you cannot do a short sale without all lenders with a secured interest in your property t signing off. When you have two lenders and not enough equity to offer the second more than just a few cents on the dollar, then the second lender does not have a lot of incentive to agree. Some second lenders will only agree to a short sale if the borrower agrees to a personal note. Either way, the lenders will not entertain any short sale negotiations until an offer is on the table. You'll also have to submit a short sale package to substantiate why the lenders should take less than what it owed. My recommendation would be that you retain a real estate professionals with short sale experience as trying to do this on your own is very difficult, time consuming and frustrating. You also want to consult with a tax professional regarding the tax consequences of a short sale (lenders have to issue 1099 for the amount of the debt that is forgiven). While there's a tax bill under consideration that might change some of that, there are limitations as I believe the Mortgage Forgiveness Debt Relief Act would only apply to purchase loans (i.e., loans that were given at the time of the purchase as opposed refinancing or post purchase- that's what I have heard).
If the property is foreclosed by the first lien holder, then the second will most likely end up with nothing as the proceeds from the bank foreclosure sale will most likely not be enough to pay even the first, let alone the second. While a short sale will affect your credit score, a foreclosure will be a lot worse.
Good luck to you.