In a real brokered convention the delegates get to break away from the candidates they have been selected/bound to vote for and can excercise free will. Although it depends who they are and how the individual state selection rules work, you would think they are more likely to be part of the Republican base and, by implication, hardcore religious fanatics. Party unity and electability have every chance of going out of the window - Chris Christie would have no chance but it's how Santorum could get the nomination - and even he's a Catholic.
Anyway back to Dave; I would imagine Obama's probably a little right wing for Cameron's taste.