The Real Clear Politics Average of public opinion polls has shown a steady increase in support for the ACA since the November election. According to the average 48% of the US public now support the law while 43.8% oppose. In previous years the law had consistently poor support from the public. The few of these polls that asked the reason for the poor support of the law (which I have chronicled in previous posts) showed that a significant number of those opposed it because the law was "not liberal enough." When this number is added to those who support the law, you have a majority of 54%. This number has been consistent throughout all of the polls that have asked this question.
These polls do not always specify which changes to the ACA would be needed to make it more liberal. One poll from May 2016 by the Gallup organization (and summarized by Philip Bump in the Washington Post) did ask respondents about their attitudes toward implementing a single payer plan. The graph above shows that about 55% support single payer with surprisingly 41% of Republicans supporting it. This number is close to the 54% I found who want a more liberal healthcare law. I'm going to make a leap of faith that those who want a 'more liberal' healthcare really meant a single payer plan.