The phrase "little publicity" means that something or someone has not received a lot of attention or promotion from the media or public. Full definition
There has been very little publicity for the game as of thus far and it has got some fierce competition, assuming it hits its launch window. (ps3attitude.com)
The recovery plans requested in 2010, meanwhile, have received little publicity. (reuters.com)
It's a movie that despite little publicity opened at number 8 at the domestic box office this past weekend. (johnhanlonreviews.com)