"A recently published authoritative letter from the U.S. Customs and Border Protection Agency (CBP) addressing the TN nonimmigrant visa category offers new and definite insight on the CBP’s policy for determining immigrant intent. In the letter, dated April 2008, the Executive Director of Admissibility and Passenger Protection Programs details clearly that filing an immigrant petition (I-140) alone is not automatically considered a demonstration of immigrant intent, and aliens with pending I-140s may still be admitted into US with a TN visa."
Under current CBP regulations, it seems that the current policy is to allow people to enter the country under TN status even if they have a pending green card application.
Also be cognizant of http://www.hooyou.com/tn/limitations.html :
"...a pending or approved employment based immigrant petition (Form I-140) or family based immigration petition (I-130) does NOT impute immigrant intent. The TN alien is eligible for TN extensions & to be admitted as a TN alien until the adjustment of status application (Form I-485) is filed or the applicant applies for the immigrant visa. While other types of status holders (such as H-1, L-1 or O-1) may apply for Adjustment of Status (AOS) as soon as they wish once entering the country, those of TN status have at least a 30 to 60 day waiting period upon entering the United States before they may apply for AOS. Any applications before this waiting period is over will be considered an attempt to gain fraudulent entry by the USCIS. Additionally, the U.S. consulate may deny a TN visa application if the alien has previous applied for an immigration petition or AOS. Those on TN status who wish to file an I-140 immigration petition should not travel outside of the country because they will encounter issues upon their re-entry. If an alien on TN status has an approved I-140 petition and is currently waiting on their AOS petition to be approved, they must be sure to apply for Advanced Parole to travel outside of the country. For more information on AOS, please click Adjustment of Status."
These are Executive Branch regulations and can change easily unlike the fairly set-in-stone congressional statutes, so it's best to keep up to date on what the current state of affairs is.
It's best to hire a good immigration lawyer and ask them how to proceed.