gmail nightmare

Out of the blue my iphone started telling me my gmail password is incorrect. This is impossible, the password hasn't changed and it's been saved in the iPhone along with all my other various icrap (ipad, imac, macbook, etc.) which all work just fine. No matter what I did it insists the password is wrong. I deleted the account and readded it - same nonsense. I tried setting it up as a "Google Account" and also as a manual IMAP account. Both insist the password is wrong even though it isn't (I can login through safari for example). I have tried myusername and myusername@gmail.com under both configuration scenarios with the same result. The only thing that varies is that with a manual IMAP configuration sometimes isntead of saying hte password is wrong it says the server is "not responding". This is also complete nonsense, my iPhone is on the same wifi network as all my other devices which work fine.

This is infuriating and it's turning my iphone into a worthless paper weight.

Can anyone explain?

Thanks.