The electronics suppliers are not used to this kind of traffic. I remember Ti's website grounding to a halt when I was first in college when they released a new kit for free, and in the past when they have done coupons for half off certain high value items. Interesting side note, Ti for its free samples uses Digikey to process them (same address, same exact boxes, packaging and onetime when I ordered a free sample I got Digikey note rather than a Ti note :P)
The traffic for those websites generally is very low, I can't imagine that they are ready for anything to what they are seeing right now.
I do wish they had also launched with Digikey my favourite electronic parts distributor. Their shipping is always top notch and their service is absolutely fantastic.