Updating steam offline.

I'm afraid I can not help you any further than saying wait for it to work. It could be that your issue is related to the problem on Steam where you sometimes lose your connection to the Steam client, even if your connection is stable and works otherwise fine (not talking about maintenances or the usual technical issues). I don't know what causes this but waiting has helped me before. Perhaps someone knows better.

Try deleting ClientRegistry.blob file in steam folder and then running steam, it should rebuild properly :)

In addition to what the others said, you might want to check if the firewall hasn't blocked steam from going online (or any other program that has a firewall such as avg)

Tried using a wired connection rather than wifi?

That was happening once to me. Problem was low disk space.

Valve is trying to make changes to Steam to deal with the issue you're describing. To successfully complete the update, you need to temporarily disable real-time antivirus protection. After applying the Steam update, you can turn real-time protection back on.

Source: http://store.steampowered.com/news/10310/

(Edited for accuracy. I hadn't actually read the news since the first mention of AV problems and thought they were getting it fixed.)

try F5

If what Olde says doesn't work, try this: go into your Steam folder and delete everything except Steam.exe and the folder Steamapps. Run Steam.exe and wait for it to recover the client files.