When left wing critics use the term "neoliberal" they are, at best, amplifying the confusion caused by the use of "liberal" in Europe to mean what we call "conservative" in the United States -and more usually pushing a confused political analysis. European "liberal" parties claim to favor "liberalized market rules" (deregulation), free enterprise, small government, and other policies American think of as "conservative" while what we call liberal (see JFK's famous speech) is much closer to what is called "social democrat" in Europe. When economists from the International Monetary fund tried to impose market liberalization on developing nations in the 1980s, left wing critics called them "neoliberals" and that name was then applied more broadly to Reagan's Republicans and Thatcher's Conservatives and similarly aligned right wing "pro-market" political groups. But these groups are not really for free markets and small government at all. In the 1940s, segregationist Dixiecrats claimed to be against "big government" when they tried to stop the Federal government from protecting the civil rights of African Americans. The same line has been adopted by all sorts of other criminals who don't want the government to interfere with their criminal acts.For example, the Koch brothers don't want "big government" to prevent them from pouring benzene into rivers when it would cost them actual money to run their factories properly. On the other hand, they do want government to impose confusing and costly regulations that prevent wind turbines from competing with their coal plants. They hate big government regulating finance to prevent fraud, but they love $1 trillion a year in tax subsidies of the rich. Just like their tea party front men who want the government to "keep its hands off medicare", these "neoliberals" are for big intrusive, oppressive government that protects their privileges and steps on anyone who disagrees. Even the "neo" part is wrong, because you can find exactly the same hypocritical support for "free enterprise" from English right wingers of the mid 1800s. Those advocates of limited government cheered when the British Navy bombarded Chinese cities to stop the Chinese government from imposing burdensome regulations on English narcotraffickers (yes, that really happened , the Zetas must be envious).
So "neoliberal" mixes up European usage of "liberal" with the American use and also gives too much credence to the claims of right wing authoritarians, con-men, racists, polluters, and monopolists to be for "free markets" and "small government". But it's actually worse than that, because there is a completely different American use of the term "neoliberal" - something that apparently is too complicated or too inconvenient for our left-wing theorists to understand.
In the 1980s, a faction of the Democratic party started calling themselves "neoliberals" to mean "new liberals" in the American sense. They wanted to both contrast themselves with the "old liberals" (like Ted Kennedy) and also compete with the "neoconservatives" who came to power with Ronald Reagan. The Reagan neoconservatives are more in line with what leftists mean by "neoliberal" ( see how stupid all this is?). The Democratic Party neoliberals were people like Gary Hart, Bill Clinton and Robert Rubin and they promoted supposedly "market friendly" methods for attaining the traditional American liberal goals of equal opportunity. Whatever you think of those neoliberals, and I don't think all that much of them, they believed themselves to be following the political platform that John F. Kennedy proposed not the one advocated by Ronald Reagan. Robert Rubin who is the "neoliberal" that the left loves to hate deregulated banks (catastrophically) but now says the primary problem with the US economy is that labor unions are weak and taxes on the wealthy are too low. A great deal of left-wing polemic is written as if Democratic Party neoliberals were from the same movement as neoliberals like Margret Thatcher. If your political analysis cannot tell the difference between a Robert Rubin neoliberal and George W. Bush or Augusto Pinochet neoliberal, something is wrong with your political analysis. For some left wingers, the confusion is very convenient because they claim both groups just to be the same evil, imperialistic, capitalist, bad guys and this can all lead up to their favorite theory "Obama = Bush". Everything tied up in a simplistic story that makes left wing theorists the brave truth tellers, the heroes of their own narrative.
Marxist academic David Harvey and similar ideologists have developed a theory around "neoliberalism" which, at least to me, exposes many problems with what remains of the "left". According to them in the 1980s Ronald Reagan and Margret Thatcher led a "neoliberal" counter-attack on the welfare state/New Deal that rolled back the gains obtained in the post-WWII period and instituted a brutal era of corporate power and collapsing living standards. There is a grain of truth in this theory but that grain is buried in a mountain of bullshit. First, it's important to remember that the high point of the post WWII New Deal era in the United States featured a racially segregated, sexist society with an economy that, in the USA, depended on unsustainable military spending and environmental destruction - even more so than what we have today. It's really fascinating to see that era held up as a golden age by people who claim to be such revolutionaries. If we take 1970 as the start of this supposed "neoliberal" offensive, we should recall that the US feminist movement had barely started, Cointelpro operations of the FBI were attacking civil rights organizations, RFK, MLK, Malcom X, and Fred Hampton had just been assassinated, the USA was engaged in massive slaughter of civilians in Indochina, pretty much all of South America was ruled by right wing torture states, and China was suffering through the horror of the "Cultural Revolution". Save the nostalgia, I'm not interested. In fact, the biggest change in the world economy since then is that there are now hundreds of millions of middle class Indians, Chinese, Brazilians, and other "third worlders" and India and China are global manufacturing giants. That's not exactly what Maggie Thatcher had in mind. Of course, our era is far from paradise and some things have gotten worse, but the nostalgia left, with its mythology of the good-old-days, its Marxian jargon which is intended to make users of the jargon appear to have some sort of expertise and authority, and its tendency to confuse labeling with understanding is not going to get us anywhere better.
We don't need the term "neoliberal". Let's just call them Republicans or right wingers and move on.