Probably not. It might have been possible to buy a little more time in court if you filed an answer, but at this point, the judge is finished with his or her work. All that remains is for the sheriff to come out and supervise the removal of your property. The judge is unlikely to withdraw the writ after it has issued. Your inability to find somewhere else to go is not a legal justification to stay in the landlord's property once it has been determined that you were not in full compliance with the lease.
The landlord does have the power to postpone the sheriff's arrival or cancel the move-out altogether. However, even if you pay what you owe, the landlord is not legally obligated to let you stay at this point. If you can get the landlord to agree to let you stay, you should try to get the landlord to promise to cancel the move-out in exchange for the immediate payment of everything you owe.
If you cannot get hold of the landlord and reach an understanding, you need to start prioritizing your property and get as much of what is valuable to you out of the apartment as soon as you can. Otherwise when the sheriff comes to enforce the writ your property will be placed on the curb, the locks will be changed, and you will have to guard your possessions from the neighbors and other passersby so that your things don't get stolen before you can get them moved somewhere else.
