To Keynesians, the short run is always more important than the long run, so it's impossible for them to have a "credible" long-run commitment to deficit reduction. Even today, prominent Keynesian economists are demanding more "stimulus," but the economy is not in recession and the budget deficit (which is "stimulus" to Keynesians) is already over $1 trillion. What happens if the economy slips into recession in 2013 or 2014? The Keynesians would surely break any budget deal and push for a $2 trillion deficit.
Edwards doesn't use the term "time inconsistency," but that's clearly what he's talking about. When I read such sweeping generalizations, the counter-arguer in me tends to look for counterexamples. The only one I could think of in recent U.S. history was Larry Summers and a few others persuading Clinton in 1993 to rein in the deficit in the short run. That's when Keynesianism was at a low point, though, and it wasn't even clear to me at the time that Summers was a Keynesian.