there are several services here (and I'm sure in other countries too) where you have a web page and can send messages for more or less money. look for "send sms" on Google and I'm sure you'll find some. The carrier may offer a web based service to which you can connect and send messages to.
Sending sms from a web page is nothing new, not paying for it is :). Try to understand the idea of giving stuff for free to your users. The number of the users will increase exponentially (well, depending on the service you're giving) .