It seems premature to assume they can fix the problem with code changes alone. If that's the case, the performance drop will likely be beyond acceptable. The required changes could make the vehicles physically unsafe to be on the road (think, being unable to accelerate out of danger's way because now you need 60 seconds to go from 0-50 km/h). If the option for a compromise between performance and regulatory requirements is already possible with the current hardware, wouldn't the cars likely have already shipped as such?
It seems much more likely that there will be parts replacement involved, and we may soon discover that the entire engine must be swapped out. This is unlikely to be feasible for cost, but bricking cars to intolerable driving conditions is also not enough. It's going to be really interesting to see how this develops. Done properly, this would probably be the end of VW. So I'm sure we'll see some half-assed solution that doesn't work for the consumer, but lets the company survive for a few more years until they finally collapse from consumers taking their future business elsewhere.