Very quickly, I whipped together the first prototype using the tools I'm already familiar with: Python/Flask and Google App Engine.
I designed my system to scale elastically to the load, while scaling down to zero instances when nothing was happening, helping me to save costs on this prototype. Every hour, my system polls the URLs in the database and fans out updates to all users who are subscribed to that feed. Thanks to autoscaling, I was able to load test the system with over 1000 feeds, and these heavy load spikes were absorbed by the system.
Without re-architecting the system, I can handle thousands more feeds and users, as well as increase the polling frequency (respecting feed TTL of course).