This article from the Harvard Gazette details Niall Ferguson's speech to seniors during the Phi Beta Kappa exercises. He talked about the relationship between the United States and the United Kingdom, and the possibility that the influence of our shared heritage might be coming to an end:
Moreover, in its essential outlook and national character, the United States "remains indelibly a British creation," Ferguson said. Despite its division between church and state, America continues to define itself by the doctrines of evangelical Protestantism that formed the spiritual heritage of its earliest settlers. Americans still see themselves as a chosen people driven by Manifest Destiny, nationalism, and the work ethic, a set of values "terribly familiar to historians of the British Empire." America even finds itself waging wars on the same battlegrounds (Asia, the Middle East) in which the defenders of the British hegemony struggled.
The problem is that as America becomes more like Britain, Britain is becoming more Europeanized, undergoing a marked decline in religious faith, a growing skepticism about patriotism, and developing a more relaxed, more European attitude toward work. The transformation may help to explain the current unpopularity among citizens of the U.K. of Blair's support for the Iraq War.
More importantly, it is unlikely that the United States will become a global empire like the Britain of old. Besides the increased importance of national sovereignty, there are the two domestic constraints of national finances (which, without financial exploitation of occupied countries or severe sacrifice by the American people, will not support such an expansion) and public opinion (which seems to be stuck in a "Fortress America" mode, where increased domestic security and short military interventions a la Afghanistan are the norm). And unlike Britain, which was constantly competing with other European powers of similar military strength, the United States stands head and shoulders above the other countries of the world. As a result, it truly does not need empire.
Regardless, the growing Europeanization of Britain, along with Eastern Europe1 is real, and will only continue as American military forces are transferred from Europe to other parts of the world. There is the possibility, however, that the United States will continue to follow Britain, eventually becoming "Europeanized" itself.
1 It may seem contradictory to speak of the "Europeanization of Eastern Europe." I would argue that the term "Europeanization" refers to becoming part of Western Europe.