I have tried, but it works only in IE,that too if we use NTLM.
Looks like, Windows wont share NT username to any application unless it is local to the system.
This is not true. If you use NTLM authentication (which is supported in many browsers, not just IE) you will have an authenticated subject that includes the NT name. You can never get the password.
You should be aware that NTLM is not a very secure technology; as of Windows Vista Windows has disabled NTMLv1 by default. You might consider Kerberos and SPNEGO as a more secure option.
Easier than these options is to use LDAP and AD as your authentication repository, then you can just ask people for their credentials (SPNEGO can be a bit difficult to troubleshoot).