I get my orders from them in 2 days. If you ordered on Saturday and will receive it on Thursday, then technically that is 3 days. Ships on Monday, Tuesday is day one, Wednesday is day two, and Thursday is day three. I really wouldn't complain about one day. Out of curiosity... was the delay caused by Diapers.com or UPS? If they shipped today, anything that UPS does is really beyond their control.
Here's what their site says:
2-Day Shipping
We ship via UPS and several other premium carriers to provide expedited service. When you order by 6pm on a business day, most orders will ship the same day and you will receive it in 1-2 business days.
Click to find out when you will receive your order. However, note that some items including those shipped directly from the manufacturer will take longer to arrive; ship times for these products will be noted directly on the product detail page.
Note: You must order by 6pm in the time zone to which you are shipping.
The following orders may result in delayed shipping:
Incorrect shipping address
Shipping address does not match billing address
Payment delay or issue
Orders held because they contain a large quantity of a single item that would cause inventory depletion (note: this is an infrequent circumstance)
UPS failure to deliver (e.g. severe weather conditions)