Republican strategists Ed Gillespie and Whit Ayres write:

Asked whether they would prefer a system where most Americans get their health care coverage through the federal government or a private insurance company, voters favored a predominantly private insurance system by almost exactly two-to-one, 60-31. The Republican margin was almost exactly 8:1 (87-11), and Independents 2½:1 (61-24). Democrats diverged, favoring a system where most Americans get their coverage through the federal government by 15 points (37-52).
This explains important splits in two subsequent policy-related questions. Forty-seven percent (47%) agreed with the statement “Americans need a public health insurance plan administered by the Federal Government to expand choices and control costs by competing with private insurance companies” versus 45% who agreed with the statement “a government-run health insurance plan will use taxpayer subsidies to undercut private insurance rates, and force private companies out of business, resulting in everyone going into a government-run plan.” But when you break this essential tie into partisan IDs, a majority of Independents (51%) agree with the undercutting argument, more in line with the vast majority of Republicans (67%) than the mere 23% of Democrats.
While a plurality in the survey (49%) agreed that “to increase the number of people with health insurance coverage, the federal government should require all employers to provide health insurance for their employees, or pay to support a public plan that would cover their employees” versus the 43% who agreed “if the federal government requires all employers to provide health insurance for their employees or pay to support a public plan, employers will likely drop their coverage and shift their employees into a public plan.” That plurality, however, is driven by the overwhelming agreement of Democrats (66-27). Independents (39-50) and Republicans (36-55) were more likely to agree with the private-to-public shift argument.
There is an inconsistent gap between the strong preference for a system where most Americans get their health coverage through private insurance and the pluralities favoring the employer mandate/tax and the public insurance plan. If the public better understood the privateto- public shift that would result from these two policies, support for them would likely drop significantly.

Also worth noting is a recent Kaiser poll that suggests how malleable public opinion on health care is (see especially charts 21-26). So, for example, respondents split 71-26 percent in favor of a mandate for employers to pay for their employees’ health costs — but 65 percent of the majority switches sides upon hearing that a mandate might cause layoffs, and 78 percent of the minority switches sides upon hearing that a mandate would make life easier for companies that already provide insurance.

Both polls via Gary Andres.