Actually, nobody loves SFGovTV. When I post YouTube stories about arts organizations, the views all depend on whether they promote it on their own Facebook wall, web page, or Twitter feed. SFGovTV doesn't have many fans- we're a service organization without any brand identity.
I recommend -
Do not post video after 3pm. People won't see it and won't have time to share or re-tweet before the end of the work day.
No thumbnail on the video link? Delete it and post it again. And if it doesn't work, wait an hour and try again. You have to have a thumbnail to get clicks.
Do not make multiple posts at the same time. Facebook doesn't share if you overshare. You have to allow a few hours gap to make sure people see the video, instead of your other reminders.
Post to your own wall. Don't sign in as "you" and post to your organization's wall. You have to post as the organization for the video to be seen by your fans. Even if a fan posts on your wall before you do, you have to go ahead and re-post the video as the organization to spread it.
Post it again first thing on the next Monday morning. "Hey, in case you guys didn't see this last week…"
It works. Trust me.