After Google enabled by default encrypted connections to Picasa Web Albums, it started to become obvious that all Google services will soon switch to HTTPS. Probably the most unlikely candidate for this change is YouTube, Google's biggest bandwidth hog, but the unexpected happened: go to a random video and you'll notice that all the resources use HTTPS.
YouTube API's blog has recently announced HTTPS support for embedded videos. "We're planning a gradual expansion of HTTPS across other aspects of the site. The first place you may see HTTPS YouTube URLs is in our various embed codes, all of which currently support HTTPS in addition to the standard HTTP. Anyone can try HTTPS with YouTube embeds today—simply change the protocol portion of the URL from http to https." You can also enable "use HTTPS" when you generate the embedding code.
The performance doesn't seem to be affected and, if everything goes well, YouTube will probably switch to HTTPS in the coming months.