From your Source=node/view/line.tpl I guess you are using {node_view_gui...} to load the line.tpl file inside a full view tpl file (override/template/full/myclass.tpl for example). In that case {set-block scope=root variable=cache_ttl}0{/set-block} won't work as the output of line.tpl is cached inside the cache of {myclass.tpl}
Add it to the calling tpl file as well, or use Ajax (jquery/yui) to fetch the numbers and still benefit of the view caching.
Thank you for your reply. You're right, I use node_view_gui. In fact, the calling template is the ezwebin basic folder template. I think I'll overwrite this template for this node in order to add {set-block scope=root variable=cache_ttl}0{/set-block}.
But, I don't understand what you mean about the Ajax method. Do you mean I can access eZ Publish objects through javascript ?