Less than 12 hours after Apple opened the floodgates to pre-orders, certain iPhone 6 and iPhone 6 Plus models have already become impossible to order for a September 19 delivery. The larger iPhone 6 Plus is in particularly short supply—all models in the Apple online store now show estimated shipping times of three to four weeks, and the story is the same on the various US carrier sites.
This might suggest that the larger model is more popular among pre-orderers, but that's not necessarily the case. Leading up to Apple's announcement, the rumor mill consistently agreed that the 5.5-inch version of the phone would be in shorter supply, and some rumors even suggested that the phone would launch after the smaller 4.7-inch version. That was basically how things played out the last time Apple introduced two new phones at once—the iPhone 5C was available in abundance at launch, while the iPhone 5S (and the new TouchID sensor that allegedly created a manufacturing bottleneck) was much more difficult to find.
AT&T told Re/code that demand for iPhone 6 models was higher than it had been for the iPhone 5S launch a year ago, or for the iPhone 5 launch the year before that. Apple usually releases official iPhone sales numbers within a week or so of the launch date, and so far every iPhone launch has managed to outstrip the one before.