The day after Democrat Kathy Hochul scored an upset victory in a special election deep in upstate New York’s Republican territory, former President Bill Clinton was getting real chummy with Congressman Paul Ryan, whose plan to privatize Medicare was widely seen as costing the Republicans the race and imperiling as many as a hundred GOP House seats in next year’s Congressional elections. Backstage at an event on national debt at the Peter G. Peterson Foundation, Clinton told Ryan, “I hope the Democrats don’t use it [the election] as an excuse to do nothing” on Medicare. Clinton may be right—but not in the way he seemed to mean.

The Democrats do need a winning Medicare plan, but they’re not going to find it by meeting Republicans in the middle (as Clinton’s former budget chief Alice Rivlin does with her Ryan-lite voucher proposal). And they’re not going to find it by only running against Republican ideas.

Indeed, the main strategy Democrats seem to have adopted in the wake of Hochul’s victory is to force Republicans to double down on Ryan’s agenda and pray that voters, particularly seniors, remain alarmed enough about the right’s shock doctrine tactics to throw the bums out. That might be a winning electoral formula, but how about some leadership and a plan to deal with rising healthcare costs? Where Democrats should look is Medicare itself—Medicare for all.

The chief lesson Democrats should take from the backlash to Ryan’s Medicare privatization scheme is that when faced with a choice between a market-based healthcare system and a government-run plan, voters overwhelmingly favor the latter. Nearly 80 percent oppose cutting Medicare benefits and two-thirds support raising taxes to continue to fund them. That’s because Medicare works—not perfectly, but compared with private health insurance, it’s far more efficient at keeping down costs while ensuring a baseline of coverage.

Contra Ryan, the problem with Medicare is that it’s not big enough; in countries like France and Canada as well as the United Kingdom, where government plays a much bigger role in financing healthcare and bargaining down prices, healthcare costs are about half what we currently spend, and they have comparable or better health outcomes.

Instead of just hoping that Republicans continue to play to their Tea Party base and implode in a general election, Democrats should be taking this moment to lead and to educate, not just on the practical virtues of Medicare for all but on the principle of social solidarity behind it.

They have the perfect opportunity now that Vermont Governor Peter Shumlin signed a single-payer healthcare plan on May 26. Vermont’s plan isn’t the single-payer system die-hard advocates want (there’s no funding for it yet, for example)—but it’s a start. If Vermont succeeds in providing its citizens with quality healthcare while keeping costs below market rates, other states may emulate its pioneering plan.

But in order to act as a national model, Vermont will need a federal waiver to bypass some of the requirements of the Affordable Care Act, passed in 2010. Obama has said he supports granting such waivers, but under current law he can’t do so until 2017. Vermont Senators Bernie Sanders and Patrick Leahy and Congressman Peter Welch have proposed legislation that would move the window up to 2014. That’s a bill worth going to the mat for.