Eww! I just heard someone use that phrase on MPR, talking about the water supply in Cottage Grove, Minnesota (if you're interested, read or listen to it HERE)
Literally, it means you can sleep confidently, without worrying. How odd.
And it ALWAYS make me doubt what's being assured. I suppose because it feels like a put-down: don't worry your pretty little head about that, darlin'...in a treacly, John Wayne voice...you're just too dopey to understand all the ramifications here.
For me, it's too Jesse Ventura. When he said we should rest assured, it sounded like he was selling snake oil. What a colossal embarassment he was for Minnesota. We honest-to-gawd elected a wrestler? Eww!