Although I don't expect this sort of nuance to emerge during Republican primary season, I hope the Democrats take this on during the general election campaign. The party has failed to combat claims its members are anti-market when that couldn't be further from the truth. Many liberal policies simply aim to make markets work better.
Take, for instance, health care. Setting aside any moral claims about whether or not we should provide some sort of universal health care system, it seems like it can be justified on market-based ground in a number of ways. Democrats should use this to counter arguments the system is somehow the antithesis of a "free" market economy.
First, some broader scheme is needed to ensure people internalize the externality of people that can otherwise afford it failing to get their own health coverage. Although some Republicans are happy letting the uninsured die, most people, I think, find something morally repugnant about denying health care to someone in a time of need. Without a single-payer system or some sort of mandatory insurance scheme, this arguably creates the incentive not to pay for health care--if you get sick, someone else will have to cover the costs of it anyway. By mandating everyone that can afford it pay into the system, we can minimize this problem and incentivize people to better care for themselves and others. This creates "skin in the game" as the Republicans are so fond of saying.
Second, this will arguably create a more flexible labor market. People often feel tied to their jobs because of the health benefits. If we uncouple health insurance from work, employees would have much more freedom to move workplaces, and employers would have much more freedom to add employees (no longer concerned with the increasing cost of health benefits). Wages would also rise because health care is no longer included in our total compensation.* Although this will seem foreign to most workers, the deep connection between work and health benefits is the result of an historical anomaly anyway--it started when the Roosevelt Administration imposed wage caps on workers to prevent inflation during WWII.
* Whether this is a net positive or negative for the pocketbook of workers depends on the ability for cutting health care costs which in turn depends on which system we implement.
Moving away from healthy care, a similar argument can be made for a broader social safety net. Republicans often talk about the need to stimulate "innovation", but they often focus on tax policy. This seems misplaced. Most people are risk-averse. What's keeping them from quitting their job to create a start-up is likely not that they're worried taxes will cut too much into their profits, but that failure means losing their house and ability to care for their family. If people knew a risk like this wouldn't mean economic devastation, they'd be much more likely to take it. Obviously we need to maintain some tradeoff between risk and reward, but it seems like most mainstream arguments about the topic fail to take into account what we can do to better balance the risk part of the equation.
In theory, markets can help us by allowing us to efficiently allocate resources to better all of society (not, as some people seem to want them to act, as some sort of Darwinian accounting system). Unfortunately, they sometimes fail to work. I personally think we should use the law to help fix these problems, but there are certainly plausible argument against that--many professors at GMU could make good ones.
But whether or not liberal proposals make policy-sense, Democrats should at least emphasize their heart is in the right place. Whatever their viability as a policy matter, their goal is usually to correct some perceived market failure to make things function better. Republican policies that focus on helping business instead of markets work directly counter to that goal.