Q:

What is the Amazon EC2 equivalent of the AppEngine Channel API?

If any.  I. e. if there is something that is only roughly similar, I would appreciate if you could characterize what are the limitations and differences.

A:

I think the closest you get is Amazon's Simple Notification Service which offers some of the same characteristics of Google AppEngine's Channel API. The big minus here is the lack of JavaScript library to utilize this from a browser. Someone asked about JavaScript support, but didn't get an answer. 
One other option would be to deploy a server with WebSocket and/or Comet support like Glassfish. You will not get infrastructure provided by Amazon, but still is a viable solution. 

A:

SNS does not seem to be the right solution. The right solution is, or would be if it doesn't yet support it, for SQS to provide an HTTP API to pick objects off a queue.

