First thing to try is to reboot your device... On the Droid Maxx, holding the power button for the count of ten is supposed to be like a battery pull.. Power the device back up and try to send a text.. If that doesn't work.. Then I'd try going into settings, apps, all, now scroll down to messaging, now.... If you have texts that you want to try to save... Select clear cache, and then force stop..
If not, clear data and force stop the messaging app..
Then I'd try to send a text again..
I should ask., are you using the stock texting app?? Is the phone stock?
Try this and see if it helps.. Let us know..