1. To convince someone to purchase something through some form of deceit. The street merchants around here are always trying to push their crappy merchandise off on tourists. The electronics company has been accused of intentionally pushing faulty hardware off on unwitting customers.

2. To force someone else to deal with or take responsibility for an unwanted person or thing. Why are you pushing Albert off on me? I don't want to spend time with that dullard any more than you do! The board of directors has been trying to push the troublesome CFO off on a different company.