Some more specifics would be helpful on this. It sounds as though this will not be a typical http server situation. As noted by Ricardo, html is not "pushed" to a client, html is requested from a server and delivered to the client.
Without knowing the specifics of the project, I would recommend reconsidering how you're thinking about this. The "pushbutton" is really the client, sending a request to the server to display something. The client can certainly send relevant information to the server to affect how the html file is created and thus displayed.
That being said, it wouldn't be bad to implement an auto-refresh solution to this as Ricardo describes. Depending on what you're doing, however, the lack of a real-time system could be irritating.