Well...let self-described neoconservative leaders do it for you:
Irving Kristol (the Godfather of Neoconservatism) wrote a book entitled Neoconservatism: the Autobiography of an Idea. In it he described neoconservatism as:
It describes the erosion of liberal faith among a relatively small but talented and articulate group ... (which gradually gained more recruits) toward a more conservative point of view: conservative but different in certain respects from the conservatism of the Republican party. We ... accepted the New Deal in principle, and had little affection for the kind of isolationism that then permeated American conservatism.
In 1983, Kristol wrote:
A conservative welfare state is perfectly consistent with the neoconservative perspective.
Or take the words of Irving's son, Bill Kristol:
Are we willing to say that the country is worse off because of FDR or JFK or LBJ? I'm not willing to say that.
Irving Kristol again on neoconservatism:
Its 20th-century heroes tend to be TR, FDR, and Ronald Reagan. Such Republican and conservative worthies as Calvin Coolidge, Herbert Hoover, Dwight Eisenhower, and Barry Goldwater are politely overlooked
You can call the prevailing philosophy of the Republican party in 2007 "neoconservatism"...or "mainstream conservatism"...it really doesn't matter what you call it...what it represents is something very different than what the Republican party through much of the 20th century represented.
Certainly, it does not represent a smaller federal government...with "conservative" Republicans at the helm from 2000-2006, we have seen a faster expansion of the federal welfare state than we have since the Great Society. Conservatives' (back to the Founding Fathers) old concerns about a warfare state with all its accompanying corruption and war profiteering and centralization of power is of little concern to conservatives today...and, again, I think that is the influence of neoconservatism.
My own definition of neoconservatism is a political philosophy that is based on, what Fred Barnes called "big government conservatism"...advocacy of modern-day New Deal-type domestic policies and an internationalist, interventionist foreign policy.
Political realities on the ground have changed in the latter half of the 20th century. The American and global left shifted the center aided by several factors including demographics, perceptions of greed, and control over information. One can rail and one can complain, but the fact remains that sticking to one’s view in the face of change is a recipe for defeatat the polls. To win in any endeavor over the longer term one needs allies.