Personally, I think 5 senators from each party, and 3 house-reps for each party, should be able to ask questions to the President each week. In their place, congressmen and women would be able to substitute their right to ask questions by allowing a constituent to engage the president in a question. The President does not have to answer, but it would be shown, nonetheless.
I don't particularly like the U.K.'s way of doing it because its not formatted and often involves nothing more than the parties hurling insults and the P.M. is often unable to get any words out when he/she responds.