Actually, that's not quite correct. Per the Wall Street Journal, they have locked up their core players to long term contracts so that should keep them competive in the AL East for several years. Obviously, these things are cyclical as things can change very quickly in sports. In addition, they will be recieving $30 million from revenue sharing another $30 million from media contracts and merchandise sales. And it isn't like they haven't spent money already; Stu Sternberg, formerly of Wall Street, spent $18 million to improve that god awful stadium.
However, they do have to meet a budget and their problem seems to be attracting fans, which now that they are the real thing may not be as difficult. Notwithstanding, expenses will rise and local politicians are trying to help but for long term viability they will need a new stadium; the plan for a new stadium (which included Sternberg putting up $150 million for a $450 million stadium) was shelved because of the economy.
So for the short term they will not be going away. Long term, who knows?
Ultimately, the more established teams in the bigger markets like the Yankees, Cubs, Dodgers, Phillies, Mets, Angels, etc. will have their way. Obviously, the solution is something like NFL revenue sharing (thereby, allowing teams like the Packers to survive) but in baseball that's not a possibility.