I, being a Reds fan, would equate the situation to Jason Giambi of the Yankees. The expecations are very high, and he's a highly paid player, so when he underperforms, he's going to get a little ribbing.
Cincinnati fans are no where as rude or jaded as NYC baseball fans--we wouldn't boo Junior for slumping for a month, hell, he slumped for the first half of his first season with the Reds and we cheered louder than ever we were so glad to have him--but Griffey's injuries the past two seasons, and his seeming lack of heart on the field have lit a small fire. But I would say it's more of Griffey's public reaction to the negativity that's made it an issue.
Do we want to Griffey to leave? No way, we actually love him too much. He's Cincy born and raised, and his dad was a star of the Big Red Machine. So he's not going anywhere from a fans point of view, but that doesn't say much for the GM, Jim Bowden, a notorious wheeler dealer. We just want the the gold glove Griffey who hits 50+ HR's and drives in 120+, and everything else, even the complaints about loafing to 1st base on pop flies and grounders, will disappear.