Stiglitz discusses two important issues in this clip: 1.) the idea that some want to build the banks up in such a manner that they cannot fail and the required government oversight that will surely coming along with that, 2.) the other idea that these same banks in fact need to be broken up so that we can return back to normal capitalism.
I'm not 100% sure that I'm smart enough to fully understand what he's saying, but seems like the issue is not unlike the problem of US automakers. They've now become so large and massive and despite being crappy car-markers, they are so engrained in the American economy employing millions of workers, that they are in a sense too large to let fail. Similarly, the banks that took on excess risk for profit potential, were at the time so large that when they started to collapse, the repurcussions were massive. I suppose the challenge now is that we are so far down the path that it's incredibly painful to effectively start over or work backwards.