The CWS is a pretty big event on ESPN. I'd say that the people of Omaha care about it. Not to mention the fans of the other teams that go. I'd say that it's pretty popular throughout the south and southwest.
I think two of college baseball's problems are 1. There aren't very many good Northern schools, which makes it a regionally based sport, just like Men's ice hockey, and 2. there are so many games that people only start following the team if they make the postseason, or more specifically a SR. I'm sure most schools have fans that are like "Hey, that's Texas A&M, they must have had a pretty good year." Another reason is that college basketball's postseason runs into over half of the regular season.