However, the poll did show that a plurality of respondents (41 percent) believed that a single-payer plan would result in the loss of private individual and employer-sponsored plans, while only a quarter said private plans would remain. The remaining 34 percent were unsure.

An encouraging sign for supporters of either Medicare for All or a public option is that voters appear willing to accept that those plans would mean higher taxes.

Eighty-three percent say that Medicare for All would lead to higher taxes for "most people." At the same time, 50 percent say a single-payer plan would mean that individuals and employers would no longer pay health insurance premiums.

The public perception of the three most prominent health care proposals from Democrats –– Medicare for All, a public option, and Obamacare –– is that they are intended to expand access to health care, rather than lower costs. Only 19 percent believe the main goal of Medicare for All is to lower costs, compared to 68 percent who believe it is to expand coverage.

Only 26 percent believe the intent of the ACA is to lower costs and only 29 percent believe a public option is aimed at costs, rather than access.

Fifty-three percent say that lowering the cost of prescription drugs is "extremely important," while 34 percent call it "very important," making that the top health care issue among respondents.

In a close second, however, is ensuring that ACA protections for preexisting conditions remain in place. Fifty percent call it extremely important, while 33 percent say it's very important.

Read more: 

• House Democrat offers state-based Medicare for All bill
• Middle class the winners in Warren's Medicare for All plan
• 9 ways to finance Medicare for All, none of which look that great