TN does not allow for immigrant intent, but only a pending I-485 is explicit proof that you have immigrant intent. So, an approved or pending I-140 is NOT explicit proof of immigrant intent according to the Nebraska Service Center.
But, although the NSC and the former INS has stated this, and in practice I have not heard of an issue when a TN is renewed by mail while an I-140 is either pending or approved, I have heard of issues when people cross the POE in TN status, or apply for a TN at the POE with a pending and/or approved I-140. This is probably because the CBP officers don't work for USCIS and therefore do not need feel they need to abide by their policies.
So taking this into account, if you were to apply for a TN, I suggest you apply for your TN via mail, not in person. The other option is to wait until the I-140 is denied due to financial issues, and then when if you apply for a TN in person, you may need to show the officer at the POE that the I-140 was neither approved, nor pending.
QUOTES:
"The fact that an alien is the beneficiary of an approved I-140 petition may not be, in and of itself, a reason to deny an application for admission, readmission, or extension of stay [under TN status] if the alien’s intent is to remain in the United States temporarily. Nevertheless, because the Service must evaluate each application on a case-by-case basis with regard to the alien’s intent, this factor may be taken into consideration along with other relevant factors every time that a TN nonimmigrant applies for admission, readmission or a new extension of stay. Therefore, while it is our opinion that a TN nonimmigrant may apply for readmission in the TN classification, if the inspecting officer determines that the individual has abandoned his or her temporary intent, that individual’s application for admission as a TN nonimmigrant may be refused."
Letter from Yvonne M. LaFleur, Chief, INS Business & Trade Services Branch
(posted on AILA InfoNet as “I-140 Filing Not Dispositive for TN” (June 18, 1996)).
"After considerable discussion between the Nebraska Service Center and AILA's NSC Liaison Committee, the NSC now indicates that the filing of an immigrant petition is simply one factor to consider in the adjudication of a TN extension, and should not automatically result in a denial. The NSC, which has exclusive jurisdiction over TN applications made on Form I-129, had previously indicated that NSC adjudicators were being told to deny TN applications if an I-140 immigrant petition has been filed on the individual's behalf. The basis of the denial had been that the individual no longer has nonimmigrant intent."
AILA InfoNet, “NSC Backs Off I-140/TN Policy Change” (posted on AILA InfoNet at Doc. No. 02111431 (Nov. 14, 2002).