I figured out what was happening in my case. I "floated" my new 5s. It was backed up two days before, so I was not too concerned about it. Then, when I received my new device at the store, I started the restore. As it was happening, I noticed that it was 7.0.3 and needed an update, but it was in the middle of the restore, so kinda stuck.
So, once I couldn't figure out how to get my photos back, I searched a little and ran across the following comment:
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Yesterday I needed to replace my iPhone and went to the local Apple Store. They were great and I left soon after with a new phone in my pocket. I then got home and tried to restore from iCloud and there was no backup available to restore from. I knew that my old iPhone was backed up to iCloud the previous night, so I knew it was there and only after I upgraded to the latest iOS that I was able to then Reset and Restore per these instructions.
Thus, note that if you get a replacement iPhone from the Apple Store and try to restore from iCloud that you will first need to ensure that you have the same version of iOS before you start the restore.
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Doesn't have to be the same, but it does have to be the same version or newer. (The issue arises when you try to restore from a backup created on a phone with an newer iOS than the phone you are trying to it restoring to.)
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So, thanks to both jv_oz and rander4, this was the deal for me. Once I reset the phone after updating to 7.0.4, everything came back.
Hope this option helps someone!