I don't expect Romer to turn a speech into an academic debate and in this sense I don't fault her. Nonetheless I did not find her account very persuasive.
I would start with the fact that output has bounced back more robustly than employment has. AD theories per se do not explain that differential. One simple possibility is that better management and better measurement have allowed us to identify (and fire) hundreds of thousands of low-wage people who just weren't producing much of value. That's a real shock, even if it does not qualify as a sectoral shift in the traditional sense.
It's also the case that the rate of new job creation has been especially low. Yet the nominal wages on those jobs-to-be are not constrained by previous contracts or agreements. Tell stories as you may, but it's hard for me to see that as exclusively an AD problem.
I wonder what is the behavioral postulate for how long all these unemployed workers are all staring jobs in the face yet persistently stubborn about their appropriate nominal wage. I'm all for behavioral economics, but I don't buy the necessary story here.
I don't want to oversell the minimum wage hike + unemployment compensation extension + means-testing hypothesis here, but surely it deserves a mention as one relevant factor. Those are real factors too.
I also see that wages, and the job market, are more flexible today than in a long time, with so much service sector employment, so much flex-time and part-time, and such a low rate of unionization. In most AD theories that implies the job market bounces back relatively quickly yet that is not what we observe.
A separate question is what Romer believes the major AD shock to have been. She clearly repudiates the Scott Sumner story that monetary policy was too tight. Is it all from the collapsed bubble in the housing market? Keep in mind those are paper values and that the real services from the country's housing stock haven't declined. Again, you can tell behavioral stories about the asymmetric perception of losses vs. future gains (for many people, buying a future home is now much cheaper, though perhaps they don't notice the positive wealth effect), but is that going to drive the whole cycle?
To be sure, AD is a major factor in this recession but it is not the entire story by any means. In major recessions usually it is AD and AS forces together.
Most of all, the Romer essay convinces me that current economic policymakers — not to mention many bloggers — should not be so certain they understand what is going on.
Addendum: I sometimes have the feeling that commentators on the left reject the "real shocks" hypothesis because they think it implies government can't do much to make things better. That doesn't follow. Most of what government does, for better or worse, is an attempt to solve a real rather than a nominal problem. It might imply "intervention is less effective" but it also (possibly) can imply "intervention is more necessary."