Soon a Commission on Question Time would be formed to agonize endlessly over the details. The events would lose their spontaneity. They would turn into the canned and boring presidential debates in no time. America does not suffer from a shortage of political discourse! Let the president and Congress do their jobs and perform the regular rituals of American democracy. And if it strikes the president's fancy, let him meet with the opposition and answer their questions. But don't institutionalize it. Keep the government's hands off question time.
I think Matt is misguided here. There is a shortage of political discourse in which each side is held directly and intimately accountable to the other, and the public can see the critical traction in the interaction. One bunch of attack ads versus another is not debate. One soundbite from talking points in cable versus a journalist trying to get ratings and stay likable is not debate - and gives far too much status to journalists.
I understand how this can't be done within the constitutional system. But it really ought to be done informally. Just ensure that two or three GOP retreats a year are open to the president.