Kevin Drum says a Value Added Tax would be a good way to pay for a universal health care plan. I'll add my voice to that suggestion. A universal health care program would be a highly progressive measure, so progressivity would continue to exist even given a somewhat regressive finance structure. What's more, Kevin's right that "pay or play" finance scheme make for terrible interest-group politics since the costs wind up falling heavily on certain classes of small businesses who, unfortunately, but understandably and with some justice, then wind up furiously opposing them.
All-in-all, I think this is an area where progressive politicians are going to need to figure out a way to get over their taxophobia. The sort of things liberals want to see happen require money, and that's a real political problem. Trying to get around the need to raise this money through taxes — using various kinds of regulatory mandates and "fees" — may work pretty well when you're only talking about a small amount of money, but when big bucks come into play it's probably worth coming up with something straightforward, efficient, and comprehensible and just having the fight.