Regardless if you know password, or not, its' 2 step authentication (FORCED no choice). Nothing you can do about it if you can't authenticate against the second contact!
I heard the best example of this on the radio last week. Dude said he set up a GMail account, and gave out the address. He then, gave out the password, which was the same thing as the email address. He immediatly began getting texts because people were trying to access it with his password, and he had 2 step auth set up! If you cannot understand what has happened with this, then please get off the internet, as HACKERS have forced this type of security!
If you are using a service that DOES NOT offer 2 step auth, you really shouldn't have anything important tied to it, or stop using it! If it offers 2 step, USE it! Maintain it correctly. Think about what your phone number is tied to before you change it for a better rate!