Twilio, our SMS provider, does not have a limit on the number of messages we can send. We are, however, limited to sending 1 message per second. What that means is we can send 60 messages per minute. So if have 600 text messages to send, they would all go out in 10 minutes. Our SMS provider has designed the system to maintain compliancy so as not to violate their terms and conditions; a safety system designed to prevent abuse.
More information on Twilio's messaging can be found here: Twilio's Messaging.