I encountered this problem updating Jetpack recently. I couldn't get into the dashboard to attempt to update it again. I had a "briefly unavailable due to maintenance" error as well just after running a couple updates - one for JetPack and one for PageLines theme.
Googling the error first gave me the suggestion to delete the .maintenance file in the public_html folder. It wasn't there.
Then I looked more and found this post. It let me know that the JetPack update could possibly have failed.
Then I went into the file manager and moved the \wp-content\jetpack folder into another folder. I was then able to get into the dashboard and my website started working. The theme was intact, so I gathered the problem was actually with JetPack and not PageLines theme update.
I attempted to do the update again by clicking on the error at the top of the dashboard, but saw no activity. While I had the dashboard up, I moved the folder back and everything seems to be working.
Don't know what I did that really "fixed" it, but at least my website is back up and working.