Do you have a Realtor representing you? Best to check to make sure it's not going to expire any dates that were agreed to previously or that will change any terms that all parties have already agreed to that could cause your current contract to be invalid! If it's agreed to by all parties and the lender, you may extend the date possibly. Your Realtor will draw up an addendum that will say something like "Close of escrow to be..." (and add the date). But make sure it's signed before the deadline date by both seller and buyer. Otherwise, your contract could be voided! The escrow officer/title company or attorney will need to change the prorated numbers for the final payoff to the seller's lender and also on the new loan's HUD statement as well. My suggestion...is to call your Realtor first! Good luck!
Definitely ask your attorney and if for some reason you don't have one (which is why you may be asking this on Trulia) - then hire one and ask them to send a letter asking for an extension. Worse comes to worse, ask your attorney about "Time of the Essence"... you will not necessarily be in breach of you don't meet the exact date on your contract. All states are different, but in NJ this might work for you.