The TextSecure protocol is now named the "Signal Protocol"; it's developed by Open Whisper Systems. It is the protocol used by the Signal app on Android and iPhone, and as of this week, also used by WhatsApp.
The main takeaway: text messaging, unlike traditional instant messaging, is primarily asynchronous with long-lived sessions, where traditional instant messaging is primarily synchronous with short-lived sessions.
Here is an older post where the authors of the protocol explain why not OTR: https://whispersystems.org/blog/advanced-ratcheting/
The main takeaway: text messaging, unlike traditional instant messaging, is primarily asynchronous with long-lived sessions, where traditional instant messaging is primarily synchronous with short-lived sessions.