This is definately happening. It has something to do with the phone trying to send texts as an iMessage. It is related to the new IO7 release.
I set my phone to send either as an iMessage or a text. This is something you have to do manually in settings.
I was sending messages to other iPhones and they were not going through at all. The worst part was I was not getting the 'message failed to send' until a day or so later. I was able to send and receive texts to other phones - so it is specific to iPhones.
This issue hit me Sunday, and seems to be fixed now. I did a reset on my phone and all is well. So, try that. this does NOT mean just powering it down. You need to do the thing where you hold the home button and the power button on the top. Hold them together, at the same time, for about 15 seconds. Your phone will go black and power down.
I do this once a week, to make sure the phone re-boots and gets the latest fixins. Know that when you 'power' your phone off, it isn't turning. Like all stupid 'smart' phones, powering your phone down just puts it to sleep.
good luck, y'all!