They associated themselves with the perceived more muscular liberalism of the first half of the 20th century, especially concerning foreign policy. In a 1995 Foreign Affairs piece, John Judis writes that neocons "were Cold War liberals who searched for a Truman in the 1970s and found Reagan."
The neocons' shift rightward initially brought them to the offices of Henry "Scoop" Jackson, the Washington senator and Democratic hawk on Vietnam. Later, many flocked to the Reagan administration. George W. Bush didn't campaign as a neocon, but his staff was dominated by neocon thinkers. After 9/11, neoconservatism was virtually synonymous with Republican foreign policy.
Across those decades, neoconservatives have supported myriad, sometimes contradictory policies. For this reason, Mr. Kristol describes his creed as neither a social movement nor full-bodied ideology, but rather a "persuasion." Still, there exist core neocon values, all of which relate to a notion of imperialistic democracy.
Obama opposes them all.
The most crucial feature of neoconservatism is its Manichean worldview, wherein the Earth is pitted in an urgent struggle between purely good and purely evil nations. As George W. Bush famously told then Sen. Joe Biden: "I don't do nuance."