Deregulating markets and privatizing public institutions, a couple of tenets of neoliberalism, are much more likely to be embraced by modern conservatives, than by modern liberals. Modern liberalism is fundamentally based on societal good as opposed to the good of a few. Classical liberalism developed in reaction to monarchical rule, and was a good idea for the era, but has, in essence, led to the oligarchy of a different rich and powerful elite.
Neoliberalism cannot truly be called liberal or conservative, though it does lean to the right. I consider myself a Republican, but not a conservative. I am a neoliberal. Ronald Reagan and Margaret Thatcher were neoliberals. George H.W Bush was a neoliberal. Many of my political idols were republican neoliberals. Neoliberalism is generally a balance of Liberalism and Conservatism. It is progressive, but also conservative. It is prolife, but it also believes Global Warming is caused by humans. There are two sides of the republican party... Tea-Party Twit (e.G Ted Cruz) and Neoliberal (e.G George H.W Bush).
The reason I believe that neoliberalism is conservative is that it holds to the main concepts that they believe in. This includes such ideas as reducing public spending for social services and privatization. It is a term for very right wing ideals. In fact, many people use the terms neoliberalism and neoconservatism interchangeably.
Neoliberalism is more conservative then many other liberal dealings. It uses a more hands off approach then most liberals would like to see. However it is not a form of conservatism because it still also holds a lot of the liberal philosophies with it. It is simply a change in the thinking of liberals.
Conservatism, at least as America knows it, revolves around general economic freedom and social morality. It believes in the free market, albeit there still exist regulations such as taxes and protectionism. It believes in a strict moral code, prohibiting abortion, euthanasia, gay marriage, and the like. Conservatism is inherently reactionary.
Neoliberalism parallels with Classical Liberalism, believing in true Laissez Faire economics and social liberalism. It believes in a truly free market devoid of restrictions on voluntary deals between individuals, and therefore does not support any taxation and supports a free trade platform. In addition, neoliberals believe in a more voluntary moral code that should not be enforced through government intervention. Neoliberalism is also known as Libertarianism.
Overall, American Conservatism believes is a center right, social conservative organization, while Neoliberalism is a far right, social liberal organization.
Neoliberalism is not a principle that is based on the ideas of conservatism. Conservatism is based principles of free markets and individual effort with very little interference on the part of the various government entities. Neoliberalism has a decidedly different point of view related to issues of economics and government involvement.
Neoliberalism is "new liberalism" and Conservatism is the attempt at keeping the status quo - the idea that tradition should be the primary factor regarding public policy. Regardless of what one person's perception (or the media's perception) of what the terms mean, the fact is they are different. Neoliberalism is conservative only in the sense that is a resurgence of what actual liberal ideas (emphasis, because in the U.S. The term "Liberal" means anything but) originally started out as.
Neoliberalism is actually just liberal political and economic thought. It is the simple idea that protectionism only leads to disastrous market policy, there is nothing conservative about that. Open markets create wealth and allow for small business, and small business owners to compete globally and sell their products and services everywhere. Neoliberalism would not oppose things like gay marriage, because gay marriage generates thousands of jobs for service providers such as photographers, caterers, limo drivers, hotels, etc. Open market capitalism was the single greatest factor in wealth creation in the twentieth century, and it will continue to be so in this century. Developing market economies like China and India can attest to that.