"Since 1980, the U.S. government has reduced its intervention in the U.S. economy, which has become much more of a free market. Conservatives applaud this development because they think that free-market outcomes reward talent and hard work; progressives object to the income inequality of free-market outcomes and want to use government tax and transfer policy to reduce inequality."
Most people, whether conservative or progressive, would probably agree with this statement. This framing of the issue, however, plays into a right-wing story in which conservatives are the defenders of (free) market outcomes, including the success of the rich who have made it "on their own"; meanwhile, the "dependent poor" look to the government for handouts. This has been a basic element of the right-wing playbook for a long time. Then-presidential candidate Mitt Romney was drawing on this narrative when he complained about the 47% of the U.S. population "who are dependent upon government ... who believe that government has a responsibility to care for them."
This view has two main themes: 1) Because the U.S. free-market economy rewards talent and hard work, the middle class should emulate the wealthy for their success, not vilify them; and 2) those who have been failures in the market want the government to take care of them by redistributing income from those who have been successful. We can see these themes play out on all sorts of political issues. They form, for example, the basis for the attacks on the Affordable Health Care Act (or "Obamacare"). Middle-class Americans, in the conservative view, are being taxed--forced to pay--to provide health insurance for those "unsuccessful" elements of the population who have not earned it themselves.
The conservative argument assumes that the outcomes we observe are the result of a free-market economy. However, the right-wing objective has not been to create a free market; it has been to rig government policy and the market so as to redistribute income towards large corporations and the wealthy.
For example, conservatives themselves want to use government policy to effect a different distribution of income from what we have now--a distribution that is more favorable to corporations and the very rich. A central policy objective for conservatives, ever since the Reagan Administration, has been to cut taxes on the wealthy. And by cutting government revenue, they have been able to make the argument that government programs for the poor and the middle class need to be cut in order to balance the budget.
Also, conservatives have eliminated restrictions on corporations and protections for workers, consumers, and the environment. They have attacked barriers to international capital mobility, deregulated industries, and reduced government regulations to ensure a safe workplace and a healthy environment.
Because conservative policies have often taken the form of reducing government programs and regulations, the ideology of a free market has been useful in rationalizing them. Other conservative interventions, however, have been less able to fit into the free-market mold, and therefore are especially revealing of conservatives' genuine aims. When the financial crisis of 2008 threatened the survival of the large banks, they were quick to ask for the government to intervene with a large bailout. The "right-to-work" law recently passed in Indiana, designed to deprive unions of financial resources, is an explicit rejection of a market outcome--the private agreement between management and union to require all workers to pay their "fair share" of the costs of union representation. "Free-trade" agreements, ostensibly designed to eliminate restrictions on the movement of goods and capital, have nonetheless continued to restrict the free movement of people. Even the repeal of financial regulations in the 1980s and 1990s, ostensibly a free-market endeavor, created the anti-competitive giant financial firms that demanded to be bailed out in 2008.
The realization that the economy is rigged to benefit the rich and large corporations takes away the force of the right-wing argument that progressives want to use government to "vilify" the "successful" and reward the "slothful and incompetent." When the game has been rigged, it is wrong to say that the market simply rewards talent and hard work, and the outcomes that result can hardly be called fair. When the market outcomes that we observe are unfair, we need to both change the rules for how the economy works and use the government to restore fairness.