Users swarmed AT&T servers on Tuesday as the company began accepting preorders for Apple’s new iPhone 4.

I must admit I expected a lot more from AT&T for this big pre-order day. Apple and AT&T have gone through this three times already with each major iPhone release and still they haven’t been able to keep up.

Now it seems that all iPhone 4s that were available for preorder are gone. That’s especially harsh for those customers that tried to get through most of the day and were still not able to reserve an iPhone.

Peter Cohen started his quest for an iPhone at 5:15 am ET and tried all day to reserve a phone.

With the exception of a period of time where the Apple Store was offline completely, each time I tried, the entire process would fail when Apple went to verify my account with AT&T. Going to AT&T’s Web site was similarly pointless.

CNET’s Marguerite Reardon had a great comment in her story this morning:

While no one doubts that AT&T is making good on its promises to upgrade its network and keep up with demand, the fact remains that it’s fighting an uphill battle as growth in data usage outpaces its network expansion. In other words, building out its network is more like adding sandbags in a storm rather than constructing a dam. It’s more about keeping up than changing the dynamics.

It really does make you wonder whether AT&T will be able to handle the iPhone 4 once it becomes available. Between the new iPhone, old iPhone users and the iPad, AT&T’s network is not holding up very well.