For those of you who steer free of Google apps (Google Play, GCM) on their smartphones, some progress has finally been made on the implementation of WebSocket in the popular crypto messenger. While the changes have not yet made it into the main branch, which is distributed exclusively via Google Play, a user on GitHub has created a fork which you can build yourself and load onto your Android phone.
See here for the discussion which prompted the recent improvements of the TextSecure fork. The instructions are straightforward, though it helps if you are familiar with the Linux commandline. You will have to install Android developer tools and specifically select the "production" server at compile time. The latter is a bit unorthodox and not endorsed by the TextSecure developers, so really you should only do it if you know what you're doing.
In the long term, the changes can hopefully be merged in the main version, but until then, I guess you can consider yourself a beta (alpha?) tester and contribute to the discussions here. Expect higher battery usage and possibly some connection hiccups.
UPDATE: Czech developer xmikos set up an F-Droid repo for the WebSocket fork (look for the experimental repository). It's up to you whether you trust his builds, he claims they are built straight from the source code.