C-SPAN: Booknotes With Brian Lamb- Irving Kristol: 'What is Neoconservatism's Writings On Politics, Economics & Culture'

Source: C-SPAN- Brian Lamb, interviewing Neoconservative Irving Kristol in 1995 

Source:The New Democrat

"Neoconservatism (commonly shortened to neocon when labelling its adherents) is a political movement born in the United States during the 1960s among liberal hawks who became disenchanted with the increasingly pacifist foreign policy of the Democratic Party, and the growing New Left and counterculture, in particular the Vietnam protests." 

From CSPAN 

"Reflections of a Neoconservative: Looking Back, Looking Ahead (1983)" 

Source:Amazon- Neoconservative Irving Kristol 

From Contemporary Thinkers 

"Neoconservatism is a political movement that was born in the United States during the 1960s among liberal hawks who became disenchanted with the increasingly pacifist foreign policy of the Democratic Party and with the growing New Left and counterculture of the 1960s, particularly the Vietnam protests. Some also began to question their liberal beliefs regarding domestic policies such as the Great Society. Neoconservatives typically advocate the promotion of democracy and interventionism in international affairs, including peace through strength, and are known for espousing disdain for communism and political radicalism.[1][2]

Prominent neoconservatives in the George W. Bush administration included Paul Wolfowitz, Elliott Abrams, Richard Perle and Paul Bremer. While not identifying as neoconservatives, senior officials Vice President Dick Cheney and Secretary of Defense Donald Rumsfeld listened closely to neoconservative advisers regarding foreign policy, especially the defense of Israel and the promotion of American influence in the Middle East. Many of its adherents became politically influential during the Republican presidential administrations of the 1970s, 1980s, 1990s and 2000s, peaking in influence during the administration of George W. Bush, when they played a major role in promoting and planning the 2003 invasion of Iraq.[3]

Critics of neoconservatism have used the term to describe foreign policy and war hawks who support aggressive militarism or neo-imperialism. Historically speaking, the term neoconservative refers to those who made the ideological journey from the anti-Stalinist left to the camp of American conservatism during the 1960s and 1970s.[4] The movement had its intellectual roots in the magazine Commentary, edited by Norman Podhoretz.[5] They spoke out against the New Left and in that way helped define the movement." 

From Wikipedia

I agree with the Wikipedia definition as far as where neoconservatism and Neoconservatives come from which was in the 1960s as a response to the growing New-Left ( Socialists ) inside the Democratic Party, who opposed the Cold War and the United States opposition to the communism and also disagreed with Progressive Democrats on the New Deal and Great Society and believed that those progressive programs didn't go far enough. And wanted to move the Democratic Party and the American economy in a socialist direction. So back in the 1960s and 70s, Neoconservatives were essentially Progressive Democrats who moved away from the Democratic Party because of the emerging McGovernite Far-Left in the Democratic Party.

But what I would add to this is that Neoconservatives aren't just hawks on foreign policy who oppose communism and other authoritarian ideologies around the world. They are very hawkish on foreign policy and national security, but tend to be more progressive at least compared with Goldwater Conservative-Libertarians in the Republican Party on economic policy, as well as civil rights and other social issues. Instead of calling for the elimination of the safety net like the New Deal and Great Society, Neoconservatives believes in reforming those programs with private market principles and making those programs better.

Welfare to Work from the 1990s, is a Neoconservative idea and you could also argue that it's Progressive as well.

Supply side economics where you cut taxes deeply, but don't pay for them with either budget cuts or raising tax revenue, is another Neoconservative idea.

The George W. Bush Administration was made up of primarily economic and foreign policy Neoconservatives. The 2003 Iraq War, the 2002 No Child Left Behind education reform, Medicare Part D which was an expansion not cut in Medicare that gave is the prescription drug benefit in Medicare, these are all Neoconservative ideas and proposals.

Not arguing that Neoconservatives are Progressive Democrats, they are former Progressive Democrats who are still in sync with Progressives when it comes to foreign policy and national security, but tend to be more hawkish than Progressive Democrats and believe that liberal democracy is such a great thing that it needs to be promoted around the world even though military force. The 2003 Iraq War is a perfect example of that.

But Neoconservatives are not Conservatives at least in the constitutional and Conservative-Libertarian sense as people who want to eliminate the safety net and regulatory state. Neoconservatives believe in a public safety net, but that it should be run with private market principles and used to move people to economic independency and even believe in the regulatory state and having commonsense regulations when it comes to the environment, worker and consumer safety, and tend to support civil rights laws.

Neoconservatives aren't Conservative-Libertarians on social issues or economic issues, and't aren't fiscal Conservatives either. But people who want a strong, functioning, but limited government that is used to just do the basics and help people improve their own lives. And tend to be Federalists when it comes to social and economic government programs. Perhaps Progressive Republicans, would be the best label for Neoconservatives in America.