I'd argue this will vary with dealerships. And, the pushiness would be more sales person, rather than the dealership.
For new cars, there are a couple reasons why a dealership may push a new car over a used car. The manufacturer may be providing volume incentives and the dealership needs to sale a certain number of models to meet that incentive. Or, a new vehicle has been sitting on the lot for too long and the dealership needs to move the vehicle (this is more true for used cars).
But, USED cars are a cash cow for dealerships. Either through trade-ins or auction purchases (based on the type of dealership), there's WAY more margin in a used vehicle than there is in a new car.
Unless it's a purely volume-driven dealership, dealerships will be perfectly happy to push a used car over a new car.