There are two problems with Bush's policy of fostering democracy everywhere. The first is that it's not his actual policy. Bush's closest allies include a rogues gallery of thugs and other democracy-haters. He not only stood by but actively blessed efforts by Islam Karimov of Uzbekistan and Pervez Musharraf of Pakistan to snuff out opposition parties (in Pakistan's case, even secular ones).
With Uzbekistan, Bush initiated a strategic partnership in 2002 that was supposed to be conditioned upon human rights improvements, but he waived the requirement for each of the last two years.
In Pakistan, Bush's State Department blessed an "election" that even the feckless European Union pointed out was rigged. Bush has abandoned even token pressure for democracy in places such as Russia and China.
As Chait goes on to say, this is perfectly explainable, given the more urgent goals of combating terrorism and fighting tangible wars (which requires, among many other things, deals with the devilish border states).
It's true, criticism of realpolitik can be a convenient excuse for terminal inaction, but I think it's also true (though I'm eager to be shown otherwise) that the democracy-spreading project of neo-conservatism has not produced a concomitant concern that Bush's policy of taking the offensive abroad necessitates compromise with anti-democratic nasties who incubate, well, terrorists.