3rd generation Apple TV stopped working when I set up 2 factor authentication

If you have an Apple TV (2nd or 3rd generation) and two-factor authentication for your Apple ID, then you may be asked to type your password followed by the six-digit verification code directly into the password field. Additionally, there is a time limit, after which the code becomes invalid.

Try this: First enter the characters of your password (do not submit yet), then manually request a new verification code, then append that code to the password (no spaces or other separating characters), and then submit. That should help you get passed the time limit.

You have two weeks to turn off 2FA. Seems like a good idea to me.

Can I turn off two-factor authentication after I’ve turned it on?

If you already use two-factor authentication, you

can no longer turn it off. Certain features in the latest versions of

iOS and macOS require this extra level of security, which is designed to

protect your information. If you recently updated your account, you can

unenroll within two weeks of enrollment. Just open your enrollment

confirmation email and click the link to return to your previous

security settings. Keep in mind, this makes your account less secure and

means that you can't use features that require higher security.

https://support.apple.com/en-us/HT204915