http://core.trac.wordpress.org/ticket/18719 has a working patch now.

Edit: Plugin code to do similar until patch gets in:

    wp_oembed_add_provider('#https://(www\.)?youtube.com/watch.*#i', 'http://youtube.com/oembed?scheme=https', true);
    wp_oembed_add_provider('https://youtu.be/*', 'http://youtube.com/oembed?scheme=https', false );