Depends on what's in your cough preparation. If you're using one that contains other active ingredients than DXM, chances are the quantity needed to overdose wouldn't be too high.

The DXM trip is heavily dependent on your weight and personal physical variables, so the amount it would take to overdose obviously varies. If memory serves, the official DXM FAQ states that an 'overdose' lies in the infamous "fifth plateau", which for me, I'm guessing would be about six bottles of tussin. Not sure, though. Since there's an overwhelming amount of information on the subject ALL OVER THE INTERNET (including this site), I'd recommend a quick google search.