With the fall of the Soviet Union, the end of the Iron Curtain and the Berlin Wall, and the reunification of Germany, issues concerning World War II were finally settled. As a result, US foreign policy was suddenly in search of purpose. The political reality of the Cold War had served to clearly carve out the positions of both major political parties. Democrats were typically "doves" taking softer stands in the Cold War, preferring to err on the side of "peaceful coexistence". Republicans were typically "hawks" taking tougher stands, preferring to err on the side of "security through strength". The end of the Cold War stripped both parties of their old reliable talking points and began a period of political quicksand, where the entire nation regardless of political affiliation was taking stock before moving forward.
Although Reagan's policies ultimately proved to be successful in this instance, it did not influence the political discussion in terms of where America was going next. To be more precise, there was surprisingly little weight given to the arguments of those who wanted to maintain a strong military as a means of protecting the country against any future threat. After all, what threat comparable to the Soviet Union could there possibly be? It seemed as if America was now the only remaining economic and military superpower, and this realization made Americans suddenly uncomfortable.
The old isolationist tendencies which characterized her in the first one hundred and forty years were rising to the surface again. There was a sense of relief, validation and accomplishment which accompanied the end of the Cold War. There was also the sense that while America had acted in her own best interests and self-preservation, through its considerable efforts in the Cold War, the nation had again served the better interests of the world by defending freedom and confronting aggression. In short, the majority of Americans felt the country had done its part and should now look inward and focus its efforts at home.
Being "the world's policeman" was not something Americans were comfortable with or politically supportive of. So the end of the Cold War marked the beginning of a significant military draw down. Suddenly many Republicans joined Democrats in shutting down bases, slowing equipment purchases, reducing research and development funding for weapons and reducing the size of the military's service personnel. A new age seemed to be dawning, but beyond the reduced need for defense, it seemed that there was a vacuum in terms of where American foreign policy was going.
In Russia, Gorbachev was clearer on the way forward for his country. He had helped to end the confrontation with the West which had cost his people dearly. With normalized relations, he sought to bring Russia into the world and use this new openness to build ties that would help Russia both diplomatically and economically. Within the Soviet Union, he had instituted his policies of "glasnost" (openness - permitting public discourse and criticism of government policy with an eye to moving forward) and "perestroika" (restructuring). He also coined the phrase, "New World Order" to describe his desire that the post Cold War era be characterized by historic new cooperation between the US and Russia for international good. It was a master stroke politically, as it was well received by a Cold War weary world and yet at home it showed Gorbachev's determination to find a role for Russia that would help it keep its influence.
New World Order
http://en.wikipedia.org/wiki/New_world_order_(politics)#Post.E2.80.93Cold_War_.22new_world_order.22
Gorbachev's view
https://en.wikipedia.org/wiki/New_world_order_(politics)#Mikhail_Gorbachev's_formulation
President Reagan's successor, George H.W. Bush seemed to be reacting to Gorbachev's diplomacy, and US foreign policy remained relatively in flux until Iraqi dictator Saddam Hussein's invasion of Kuwait in 1990. Out of this invasion, America's reaction and the Gulf War effort, Bush found a voice for America's version of the New World Order.
George H.W. Bush's view
https://en.wikipedia.org/wiki/New_world_order_(politics)#Gulf_War_and_Bush's_formulation
The Bill Clinton Era
After the success of Desert Storm, where the US led more than 100 nations in a UN approved mission to get Iraq out of Kuwait after the former invaded the latter, few thought that George H.W. Bush could be beat in 1992. But with an economy slipping into recession and Bush agreeing to a tax increase after pledging to not raise taxes during the election campaign, Bush was vulnerable and Bill Clinton, an unknown governor from Arkansas turned out to have the formula for exploiting Bush's weaknesses and propelling himself into the White House. See a summary of the Clinton presidency below.