Dick Cheney is, to be sure, the Bush administration figure most likely to say something ridiculous in public. Nevertheless, statements like "Last month's anti-satellite test, China's continued fast-paced military buildup are less constructive and are not consistent with China's stated goal of a peaceful rise," are all-too-typical of the American defense establishment as a whole, an apparatus that seems to operate with virtually no self-awareness. The United States has, over the past few years, reiterated its refusal to strengthen the ban on space weapons and released a new national space strategy strengthening our commitment to retaining unilateral military supremacy in space. We've also engaged in an enormous military build-up that started from a position where we were already by far the biggest spending.
Then we turn around and say we view China's efforts to enhance its military as threatening and inconsistent with the idea of a "peaceful rise." What Cheney is doing is conflating two different ideas. One is that China's rise could be peaceful, i.e. respectful of the core interests of other major powers (the US, Russia, Japan, India, the EU, etc.) and avoid a hot or cold war with any or all of them. The other would be the idea that China's rise won't be a rise at all; that the country will get richer but will just be content to be a middle-income country with no geopolitical profile that poses no challenge to American hegemony -- like an enormous Estonia. Obviously, though, if you set that out as America's "goal" for China, then China will fall short of the goal and then we'll find ourselves in conflict. No country is in a practical position right now to in any meaningful way challenge American military supremacy, but increasingly the United States is demanding (you can also see this in reaction to Vladimir Putin's recent speech) that countries actively embrace a vision of perpetual subordinate status. Patriotic Chinese (and Russian, and Indian, etc.) officials aren't going to do that.