"Unable to verify the name or password of the account" (Twitter account Mountain Lion OSX)

I recently installed Mountain Lion OS X (10.8 actually) and have been trying to configure my Twitter account to integrate it on my iMac, the problem is that when I type my Username and Password it won't let me add the specified account, it always appears the following message below the Username/Password fields: "Unable to verify the name or password of the account".

I know it may be that I type wrong my password or username, but I have checked and double-checked both password and Username and STILL get this message it has become rather annoying what does it mean? Do I have a problem with my privacy settings, firewall or something?...any help I would really aprecciate it,

Thanks in advance!