It depends on your nationality and how you apply. Canadian citizens who apply for TN status at the border can expect the process to take a few hours. However, submitting the petition by mail can take up to six months or more. 

Since Mexican TN visa applicants must apply for a visa first, getting interviewed and receiving approval can take longer. Working with a TN visa lawyer can exponentially speed up the process as you will have a better chance of getting approved without delays for missing documents or application errors. Premium processing is available when the application is made by filing form I-129 which can be used for extending an existing TN Visa for either Mexican of Canadian citizens or for initial application by Canadian Citizens.