FWIW someone is trying to create a Signal/Textsecure client for Ubuntu phone[1][2], using web-sockets, with (I think) a QML-interface and a go back-end, so once it's ready it should hopefully be relatively easily portable to desktop Linux (and if/when Ubuntu convergence becomes more than a pipe dream it should work even without porting...)
I haven't actually used it or looked at the code, so I can't comment on the usability of the interface or the security of the implementation.