If she is not your spouse, then she will not be able to accompany you on your TN visa. If she is your spouse, she can enter on a TD visa while accompanying you. The TD visa does not have work authorization so she will not be able to get a work permit. So to answer your question: Never.
However, being in the US will allow her more opportunities to interview with companies that may be willing to sponsor her on other visas that will grant work authorization.
She also could accompany you to the US in B-2 visitor status as your non-spouse cohabitating partner and effectively remain in the US as long as you are in TN status.
However, being in the US will allow her more opportunities to interview with companies that may be willing to sponsor her on other visas that will grant work authorization.
Another route is the F1 student visa to OPT/CPT.