Experience is pretty much the only thing that you can use to negotiate a bump up the spine over here. But it is always possible to make the attempt, particularly if they've put you on the lowest point.
A competing offer would be more likely to get people asking where you want to go for your leaving drinks. We're really not into the "this is your one job ever" stuff over here.
I'm assuming from the OP's post that he's talking about negotiating an initial offer, whereas your discussion of a competing offer is presumably for a current faculty member who's already on the job.