Of course we shouldn't stop trying. We just need to understand that the issue doesn't sell itself, and it might never be popular. It might never be a winning campaign issue. Or it might. I can't tell you that.
Relatedly, understand that "universality" in policy isn't necessarily attractive. I understand the theory; social security, medicare -- because everyone is invested in the system, everyone supports it. But they also predated drained-pool politics (SS was established long before Civil Rights Act; Medicare before the upheavals created by the Civil Rights Act were fully felt). Drained pool politics is strong. Too many people on the left, in my view, ignore it at our peril. I'm not saying universality can't work, but it's not a magic bullet.