my NEW Apple Watch will not accept my apple ID

Is your Apple Watch set up? If it is, unpair/erase it (it will auto backup) and set it back up. If it is not set up let, see how to set it up with your iPhone, and setting it up should auto-connect your Apple ID.

Can you confirm that you can use the same Apple ID to sign into another Apple device? Also, is the same Apple ID signed into your iPhone that you are using to pair with Apple Watch?

I found a similar situation to yours here in Support DIscussions, here is the link: https://discussions.apple.com/thread/7925842

Let me know if this applies to your problem.