What you're missing is the difference between state and federal sentencing. Under Texas rules, you can get up to half of your sentence reduced for good time. Not in the federal system. You also can't plead for time in the federal system. The judges are much less likely to go with the prosecutor's recommendation than they are in the state system. It is a very different ballgame. Because of this, Vick will serve at least 18 months. While in prison, he could also be prosecuted at the state level (double jeopardy does not apply between jurisdictions), and have to serve time in state prison after his federal time.
23 Months, with a shortened sentence for good behavior? Not sure how I feel about this as I do agree cruetly to animals is unacceptable, so I don't know if this is enough...