Amazon Echo - Push a message to the device
I know it's capable but Amazon hasn't offered it as a feature yet. If you go to the Echo web site http://alexa.amazon.com/spa/index.html#cards, Settings, Connected Home and select Discover devices, the echo will perform a command triggered from the web site and will speak when completed. I didn't have to say a word.
I've not done this myself but it seems using the Alexa Voice Service could do the trick. It allows processing of voice from any type of audio capture and sends it to the Alexa Service. It seems possible you could record the proper phrase into a sound file and send that to AVS, thus triggering the Alexa service.
It is not currently possible, but it is an oft requested feature on the AWS forums.
http://forums.developer.amazon.com/forums/thread.jspa;jsessionid=EC0D457A400B594DD0F0561EEB43A8FA?messageID=17713䔱