Last week, the United States Senate convened hearings on amending the Constitution to “better regulate” political spending. With a two-thirds vote needed in both Houses of Congress, no one expects any amendment to pass. Yet, fundamental reform is absolutely needed — and possible.

The core problem with our democracy today is that we have outsourced the funding of campaigns to the tiniest fraction of the 1 percent. As congressmen spend between 30 and 70 percent of their time raising campaign cash, they focus their efforts on no more than 150,000 Americans. The numbers for Super PACs are even more astonishing: In the 2012 election cycle, 132 Americans contributed 60 percent of the SuperPAC money spent in all races. In no conceivable way does this tiny fraction of political donors represent America.

If Congress were really serious about fundamental reform, they could fix this problem tomorrow, with a simple majority vote, by enacting legislation that would change how campaigns are funded. There are two perfectly acceptable proposals that would achieve this result: Democrats offer a proposal of matching funds to candidates who wage small-dollar-funded campaigns, and some Republicans propose to provide tax credits or vouchers to candidates who wage small-dollar-funded campaigns. Through either of these proposals, Congress has the power to remove the current dependence on the tiniest fraction of the 1 percent, and replace it with the dependence that President James Madison promised it would have — “on the People alone.”

Yet too many politicians are afraid to even mention this obvious, and obviously simpler, solution to the problem of American democracy. So we have decided to create a SuperPAC called the Mayday PAC to force Congress to face the obvious. More than a year ago, we asked experts to calculate the cost of winning a Congress in 2016 that would pass fundamental reform. That number was big. But essential to the plan was to pilot the idea in 2014. We would run a reform-based campaign in five districts, testing what works, and when we win, terrifying the rest of Congress about the potential for this SuperPAC to rally citizens to demand reform.

The cost of the 2014 pilot was estimated at $12 million. And so on May 1, we launched an experiment to see whether we could raise money through a Kickstarter campaign for at least half. We set an initial goal of $1 million in 30 days. Insiders thought this was impossible, but with the help of 13,000 supporters, with a median contribution of just $50, we crossed the $1 million mark in 13, not 30, days. That $1 million has now been matched — by two of Silicon Valley’s greatest innovators, Reid Hoffman of Linked-In and Peter Thiel, cofounder of Paypal; two of the Internet’s greatest venture capitalists, Brad Burnham and Fred and Joanne Wilson, of Union Square Ventures; and the curator of TED, Chris Anderson.

We just launched the second challenge — $5 million in 30 days. And if we succeed in that too, then we will launch the first stage of this fight to force Congress to address the immediate source of the real corruption in this democracy — not so much whether Target or ExxonMobil can speak, but the way politicians raise the money to fund their campaigns.

This is the hard work that Congress should be doing. It’s easy to hold hearings on resolutions that everyone knows will fail. It takes leadership to force debate on ideas that no one believes can pass — but must pass. That’s the leadership that Lyndon Johnson demonstrated, both in the Senate in 1957, and as President, when he forced a reluctant South to finally accept equal rights. That’s the leadership that this nation needs again. And deserves.

Lawrence Lessig is the Roy L. Furman Professor of Law and Leadership at Harvard Law School, director of the Edmond J. Safra Center for Ethics at Harvard University, and founder of Rootstrikers, a network of activists leading the fight against government corruption.

Mark McKinnon is a Republican strategist who served as chief media advisor to George W. Bush.