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They should not, if your TN application is otherwise approvable.
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Truthful facts are needed to answer your question. The fact you failed to depart at the end of your OPT will certainly be a negative factor. You need to consult with and experienced immigration attorney.
While this answer is provided by a Florida Bar Certified Expert in Immigration and Nationality Law, it is for general information purposes only and an attorney/client relationship is neither intended nor created. You should seek out qualified counsel to review your case and provide you with advice specific to your situation. Review Mr. Devore's Avvo Profile for more information about his expertise in immigration law and how to contact him to discuss your case.