So will we see more of this? Not likely. As Kevin Drum (via Bernstein) points out, it's tactically stupid for Republicans to invite Obama to do this again:
Right now Republicans have a built-in advantage when it comes to attack politics and they'd be fools to give it up. A format like this, which puts the president front and center, allows him to directly call out distortions and lies, and rewards conversation rather than machine-gun style talking points, is something Republicans should justifiably be very afraid of. Unless they're suicidal — or somehow figure out a way to take better advantage of the format — they'll never allow this to happen again. Without the noise machine, they're lost.
Beyond that, notes Ezra Klein, it's not in Republicans' electoral interests to have reasoned public discussions with Obama. These members of Congress need to run for re-nomination among Republican primary electorates, substantial pluralities of which believe that Obama is a socialist and a foreigner and a racist and otherwise unfit to be president. Not only do they despise Obama, but they're likely to regard anyone who collaborates with him as a traitor. Unless you can figure out a way to be outwardly defying Obama in a venue in which he has the microphone, it's a risky venture.