Well, what the NFL is doing to Vick isn't even related to double jeopardy -- double jeopardy is when the government tries you more than once for the exact same crime.
First of all, the NFL isn't even remotely a government agency, so it's impossible for double jeopardy to apply.
Second, Vick hasn't been tried, he's pleading guilty, so that also stops jeopardy from attaching.
Third, as Vick's employer, they can do whatever they want as far as disciplining him in addition to whatever punishment he gets from the state or the feds. If you worked at the Gap and went to jail for stealing, your boss could fire you, too, because you're potentially risking the business.
Fourth, Vick TOTALLY broke the NFL's rules! Hello? Gambling is a big no-no when you're in pro sports -- ask Pete Rose and Tim Donaghy. Even if the NFL could ignore the dead puppies and the public relations nightmare that Vick has become, they couldn't ignore the gambling.
I mean, think about it: as fans, we can ignore drugs, violence, drunk driving, strippers on a boat, etc -- but when gambling comes into it, we start to think that maybe football isn't honest anymore! If we think that the game is fixed, that's when we stop going to games and stop watching games on TV -- pretty soon, we stop wearing jerseys and hoodies and caps. That's what the NFL is trying to avoid at all costs.