Can aniline autodeprotonate?
I'm going to side with you @TheChemist. 

Your TA might be suggesting this because you need often need a negatively charged nucleophile in order to carry out nucleophilic aromatic substitutions.  

Having the nitro group in the 4 position makes the your electrophile much more receptive to attack, since the negatively charged intermediate will be resonance stabilized.  

Even if the one aniline does deprotonate another, the concentration of the deprotonated anilide will be so low (on the order of 5 x 10-28 mol/L in pure aniline, if the pKa is 27) that this will have no impact on the reaction.