He defrauded the NYT out of thousands of dollars in travel expenses. He also accepted payment for services not rendered but nonetheless represented as such, which is more fraud.
There is no way the Times would agree to press charges on either of these points. Not only would it make them look like even bigger jerks than they already do, prosecuting a guy with mental illness for a few thousand bucks' worth of expense account claims, but it would also open them up to being put on trial in open court themselves. Just imagine all the things Blair's lawyer could bring up: Howell Raines's admitted racism ("My Southern guilt probably kept me from firing a black man sooner than I otherwise would have"); their own internal hiring policies ... their REAL hiring policies; not the ones they put in the employee handbook; their unwillingness to accept the obvious signs of Blair's manic depression and act accordingly; on and on. And that would just be in the trial against Blair. He would undoubtedly countersue them, and the fireworks would be ten times worse for the Times' reputation. What's left of it, anyway.
The Times used Jayson Blair as much, if not more, than he used them. They do not want the world to catch on to that fact.