The Ray's have good support, the only issue is getting a stadium on the other side of the bay. Baseball in general in Tampa is wildly popular, and I don't see how the franchise would be any better off in Miami. Minor league baseball is headquartered in St. Pete and at least five teams have their spring training in the area and there are a load of minor league teams in the area as well.
One big issue anywhere in Florida is that the state's transplant population makes Tennessee's seem like nothing. And they all keep their allegiance to the Yankees, Red Sox, Phillies, Orioles, Cubs, Tigers... or they are not interested in sports because there are so many other things to do. And even though something like a million people move to Florida every year, almost as many move out of Florida, it's a very fluid and temporary population. Growing all the time, but it's just a really unique situation that's hard to understand unless you live(d) there.