It works correctly in x64 version for me. So you had something else broken :-) (like wrong password/login - it doesn't show errors, and then it wouldn't let you login again, because there is some bug that sometimes needs restart after unsuccessful login).
Upon login, steam sent me the code to my email. So the login was successful. I just did not get the popup window to input this code to fully log in.
I'll reinstall x64 to check again.
Tried again. All login info 100% correct. No other connection attempts made, fresh install, freshly started the program. On connection attempt I receive an email from steam with the code I need to input. But the popup window does not show. I used an app I use sometimes and forced all windows created by Miranda NG to show and it's not one of them.