The reason for the budget shortfall is that Carcetti won't take the state money for education. He doesn't do that because he doesn't want to be seen being bailed out by a Republican governor, when he has intentions to run against that very same governor for his office in a couple of years.

It's a move that first and foremost is about his career. It's the same with running for mayor-- he knows he's not ready for the job, but the window of opportunity, with Gray siphoning some of the black vote from Royce, is there now, and won't be in four years.

Carcetti might have first dreamed up the idea to run for mayor because he wanted to make a difference, but even early on we can see him playing politics with Burrell and Valchek to boost his profile, and him ****ing the blonde is a perfect example of the narcissism that leads to this career ambition-- he's watching HIMSELF in the mirror, he's clearly more in love with himself than anything else, and that's why he chooses to run, it's ego gratification.

That's the unfortunate reality of politics-- the people who ascend through the ranks are the ones who play these games, but the only people who play these games are ultimately the ones who care about career advancement more than doing the right thing.

No one in this universe is simply good or simply evil. Carcetti does make some efforts toward doing the right thing-- he turns down Teresa because he doesn't think it's the right thing for him to do as the new mayor, and he starts out wanting to create some real reform in the PD, which is why he fast-tracks Daniels through the organization. But when push comes to shove, he puts his own interests first. He could fix the PD if he takes the state money for the schools, but he doesn't, so he has to spend the PD money on the schools instead. Without spoiling anything, you'll see some of the ramifications of that decision in Season 5, and you'll notice which of his advisors really has his ear, as his decisions become less about doing the right thing and more about political expediency and furthering his career.