The trickiest post of politics is dealing with the fact that people are mostly uninformed and uninterested, and grappling with the foolishness of the average citizen.
Which is why the popularity of a policy should be looked through the lens of do people actually support the idea behind the policy instead of what the policy is called. For example Medicare is viewed favorably among the republicans but when you turn around and start asking about government health coverage suddenly the support flips in the other way and republicans hate the idea. Except that's pretty much what medicare is.
You can't view popularity of a policy on a superficial level because on a superficial level the popularity swings whatever way depending on the very specific phrasing of the question. You have to get to the core of policy and then view the popularity of the core idea to understand the popularity of a policy. Because if the policy at its core is popular you can find support for it by cutting through the bullshit, but if the policy is unpopular no amount of cutting through the bullshit will get you support. You have to actually spin bullshit to make an unpopular policy popular and you can only do that when there's nobody on the other side calling it out. Going back to the El-Sayed and Rogers example, the reason their debate was so one-sided is because El-Sayed was on the side of popular policies and could easily present them as they are. And Rogers couldn't do anything because every time he tried to bullshit something he got called out.