To be honest, I never heard of a "news fast", but, in general, a "fast" is obstaining from food and/or water, etc. for a period of time. A fast is generally for spiritual reasons, such as you wanting God to do a special work in your life or someone else's life. So, this "news fast", my guess would be like saying "I'm not going to listen to any kind of news whatsoever for ______ days, or hours. I hope this has helped you, and I hope I have the right answer.

I think you mean, "Only one day and news travels fast" This refers to how fast news or gossip can travel either by word of mouth or via the internet.