Stability, relative disengagement, superior military technology, and a belief in the transformative power of the free market were paramount. In the absence of a pressing and visible threat, at least in the foreseeable future, such policies were key to economic prosperity and its sidekick: domestic political success. No state could compete with American economic superiority, nor match its military might. Below this fazade of unrivaled supremacy however, voices of discord were brewing among non-state actors (Radical Islamists, etc.) seemingly with no vent for their message or anger. Deterring such non-traditional threats would require non-traditional means; a reality few in positions of power were prepared to face or even able to recognize.
With the Soviet threat out of the picture, the U.S. had several broad options for approaching the new security environment. All arguments aimed at the common goal of securing American principles and interests, and yet the means suggested for meeting this challenge varied dramatically. For the conservative wing (maybe site something from The New American Century org. Note that Wolfowitz, Rumsfeld, Cheney, Jeb Bush, etc. signed its charter in 1997), the new era presented the golden opportunity to aggressively remake the face of the globe in a manner favorable to long term strategic, economic, and military dominance. Increased defense spending and an unapologetic and uncompromising promotion of American interests were key to such a strategy. From the liberal extreme, the U.S. was to remake the face of the international order as well. Rather than the stick however, the influence of the carrot was to become the modus operandi. (I need to add to this don't know with certainty what the liberal stand would have been. I want to argue later that "soft power- was necessary to promote security, not just buying allies with our wealth, but that this was not the liberal stand either).