This is not insurrmountable. There are a few things you can try. First make sure your incoming server is:
imap.mail.me.com - SSL checked only Port 993 (default)
outgoing server is smtp.mail.me.com - Override default port 587 - Check SSL
Note: your outgoing port may be different based on your ISP. Try unchecking the override as well.
More Options: Use incoming...
There has been some talk about changing your iCloud password to the new requirements. This has met with some success, as has deleting the account after this is done and re-adding it back clean.
The establishment of iCloud changed a few things, and the Outlook interface needs to be adjusted to accomodate them. If you work at it a little you can settle this into something manageable.
I am personally loving the iCloud instant update across my computers, iPad, and iPhone, and consider it a major upgrade from the Mobile Me cluster. I do not deny it has been a very unnessisarily bumpy road to get here, and have great sympathy for everyone on the path. Don't give up.
Cheers: Justin