Waiting for TN mail in

I am currently in the US on a TN but have applied for a new TN as I am changing jobs. I have a start date of August 14 but still have not received my new TN. I applied around June 14. If I don't get my new TN on time to start the new job what are my options? Can I cross the border to Mexico before August 14 and apply there? If I do so, what happens to my application that is still pending? Is it advisable to go to Mexico border or am I better off going to Canada? I am closer to Mexico than to the Canadian border. I would appreciate it if anyone had some advice for me. Thanks in advance.