The manufacturing process is likely still several days as it involves more than one factory in the process. Plus shipping to the US (1-2 days) you'll end up at probably around a week in the best case. And that only if there's enough cargo capacity to add 100k units on that route (don't know how busy they are in these weeks). I'd guess it's realistically closer to 2 weeks from decision until it's in the warehouse.
It seems to me that the Echo is what amazon pushes most at the moment. They want to be in every house. I don't think they make much by selling it, it's mostly to bind people to amazon (prime and buying through the device). It doesn't make sense to constraint supply in that case. Constraining supply is used for expensive items to suggest that they're sought after. Don't think Echo fits in that category.
Even with that lead time, you know ahead-of-time when you're about to run out of supply in 2016. There's just no excuse.
That said, I just don't see too many people buying Echo. Another distracting device that tries to get you to buy more stuff on Amazon is just not something I think people want, and the speech recognition works flaky at best, even in a quiet room (my Amazon engineer buddy has one). It's just like Siri.
I had to go brick-and-mortar to get a flash drive in under an hour the other weekend. At Silicon Valley's Best Buy in SF, the in-store Echo demo had a few passersby press the Demo button, and then as soon as it started talking, they looked confused and walked away. Not a good sign.
It does make a lot of sense: When something actually isn't selling so well, running a marketing campaign saying "we've sold out" is a great psychological hack to temporarily drive up demand.
I'm here in Chicago and it's really sold out. Nothing at any of the major retailers within 50 miles of my location.
Google Home also seems to be completely gone at every store I've visited in the last few days. That includes places like Target, who usually have their shit together when it comes to inventory.
It's pretty easy to get the factories in Shenzhen to crank out a couple extra to meet demand (it USED to be a lot harder).
I call BS.