keiichi25 makes some good points.
However, I do believe that big red also has some blame to share here. I think they are falling into the trap of raking in huge profits without upgrading their network (think AT&T) whilst selling millions of smartphones every month.
Actually, any company is going to suffer this, not just Verizon, but also Sprint with their 4G network hype and people rushing to get Evo 4G and the 4G broadband they have been hyping for the last year.
You have to remember, regardless of whoever you go with, there will always be a big demand and people hopping the boat. Even companies like Blizzard did not expect a huge out turn of people on their first release of World of Warcraft and frantically trying to keep up with demand. And even with now knowing rough demands, every time they have a major patch or expansion, they suffer some serious issues due to demand. And they even had Sony's SOE/Verant model for Everquest to see the potential and still not account for the dramatic upsurge of people on the first few days.
Also, remember... No one really looked at the Droid seriously until the Verizon/Droid viral commercials. When T-Mobile touted their Android phone, Google G1 and the MyTouch series, I don't recall many people making a big deal about it until Verizon did their "iCan't" viral commercials that made the Droid phone look like the better alternative to the iPhone and it wasn't even locked into AT&T.
Also, the only serious alternative to the iPhone was the Blackberry, and even I didn't really want to make my personal phone a Blackberry. When I saw the droid commercial, I was looking forward to see what could be done. I compared it next to the Blackberry Storm on the same network and in the same region and decided to go with a Droid because it just seemed better than the Blackberry and more to my liking.
It still currently is, and now that I am with just this phone and not at my old job, while there are some things I miss with the blackberry, I still prefer the Droid over the Blackberry overall.
But like with all things, as well as the supposed belief that iPhones no longer being sold in New York due to saturation (apparently, there is an article stating this is not the case...) The fact that Sprint, AT&T and Verizon are looking at re-adjusting their stance with Data, (Even though their current data plans do have a cap) because of the demand for smartphones have, quite literally, exploded and will be even more the case if the rumor of Apple getting Qualcomm CDMA chips for a new batch of iPhone 4 is true, which means Verizon and Sprint will also be taking more data loads for iPhone users who might switch to them over AT&T for one reason or another.