I have the same problem in Opera 19 (19.0.1326.63) on Mac OS X Mavericks (10.9.1).
The live.com login/auth page is blank. Have to reload page to get login dialog. And it fails no matter what I do.
Logging in work in other browsers, gecko based and WebKit based ... So, it's not my credentials that wrong.
Anyone working on fixing this? :doh: