I had the same problem, until I logged out of the App Store and iTunes section of the settings app. I then logged in again, but this time with the Apple ID that I initially setup the News app with. Everything worked as expected there afterwards. I can't be sure whether logging in with the same Apple ID would have solved the issue as I logged in with a different one.
I noticed that beforehand, the cache for the News app was over 2Gb but is now considerably smaller having logged out and back in again.
Give it a try