With Chrome adopting the new Content Security Policy which will soon be required for all extensions, Feedburner absolutely
must adopt HTTPS. The new Content Security Policy prevents access to any external content not transferred over HTTP, which essentially kills any extensions that rely on Feedburner feeds.
HTTPS is not hard. Google clearly has the architecture in place (Google.com itself is now HTTPS-enabled for all logged in users).
Please enable HTTPS for Feedburner too.