Sticking with the health care example: Medicare was enacted over significant opposition in both the House and the Senate, reflecting significant opposition among the American people. Today, that debate has been won. Medicare is very widely popular. There's been no attempt in Congress to repeal it (unless you count the bill or amendment that Anthony Weiner introduced, just so he could taunt the Republicans for not supporting it).
We're not at that stage with single payer for all. It polls less well than does keeping Medicare. Note that even the article you link, about a poll last month, reports only that "51 percent of all adults surveyed support implementing a single-payer healthcare system in the United States." Its support drops even lower if people are asked if they'd be willing to pay higher taxes to get it. (Of course, this question is somewhat misleading because millions of people would pay higher taxes but lower-to-nonexistent other payments for health care, and would come out way ahead, but this point isn't universally understood.)
With a 51% to 43% division of opinion, I'm glad our side has the 51%, but such a bare majority isn't enough for a fundamental change.
I'm less optimistic than Bernie. It seems to me that good ideas don't spread like wildfire nearly as often as do bad ideas (Let's invade Iraq! Let's defund ACORN!).
I do agree with him that single payer and other such ideas have gained a lot in being considered more mainstream and less fringey. That's definite progress. It sets the stage for winning the debate, even if the debate hasn't yet been won.