On July 4, Harvard law professor Larry Lessig successfully completed a $5 million crowdsourced fundraising drive for his Mayday PAC to promote public financing of elections. Combined with $2 million he raised in May and another $5 million in matching money he expects to raise in the coming weeks, this will give the organization a $12 million war chest to reform the way American elections are funded.

Three quarters of the 52 Republicans who voted for McCain-Feingold are no longer in Congress

Raising $5 million in small donations for an issue many pundits have claimed isn't a priority for voters is a significant accomplishment. But the biggest challenge is still ahead: attracting Republican support for his proposals. Because it will be difficult to get his legislative proposals passed without buy-in from at least some GOP members of Congress.

When Congress passed the McCain-Feingold campaign finance reform legislation in 2002, it did so with overwhelmingly Democratic votes. The bill got support from 198 Democrats and 41 Republicans in the House. In the Senate, 49 Democrats and 11 Republicans voted yes.

But in the last 12 years, Congress has become more polarized. By my count, three quarters of the 52 Republicans who voted for McCain-Feingold are no longer in Congress. And the remaining members seem less interested in campaign finance issues than they used to be. When Democrats proposed the DISCLOSE Act in 2010 to bring more transparency to campaign donations, not a single Republican — even John McCain — voted to bring it to the Senate floor.

Lessig clearly understands the importance of attracting conservative supporters

One reason for this is that opinions on the issue have hardened since the Supreme Court's 2010 Citizen's United decision. Many people on the right agree with the Supreme Court's conservative majority (and the ACLU) that regulating political advertisements violates the First Amendment.

More generally, many conservatives are unpersuaded that "money in politics" explains Congressional dysfunction. They view the corrupt political process as an inevitable consequence of big government. And they think other reforms — such as term limits and a balanced budget amendment — are more promising avenues for reform.

Lessig clearly understands the importance of attracting conservative supporters. His standard pitch includes an explicit appeal to them, arguing that the corrupting influence of money in politics makes it as difficult to shrink government as to enact the reform ideas liberals favor. In one of his videos, he cites data from the libertarian Cato Institute on the massive quantity of corporate welfare Congress enacts every year.

And he has a point. Conservatives and libertarians like to point out that "incentives matter"; people do more of things when they're rewarded for doing so. Given that members of Congress spend hundreds of hours every election cycle on fundraising, it's clear they place a high value on campaign contributions. It's hard to believe that the need to raise millions of dollars every election cycle isn't distorting how members of Congress vote.

Yet spending taxpayer dollars on political campaigns is going to be a hard sell for conservatives. In the increasingly polarized environment of American politics, it will be difficult to convince Republican politicians to join Lessig's crusade. Given the Tea Party's demonstrated power to end the careers of Republicans who stray from conservative orthodoxy, endorsing public financing of campaigns would be a big gamble.

Yet the Mayday PAC is less likely to succeed if it winds up mostly supporting Democrats and comes to be seen as just another Democratic interest group. Partisan gridlock makes it much harder to pass any sort of legislation that only has the support of one party. And it might be years, or even decades, before Democrats next gain control of all three elected branches of the government. By then, the current momentum of Lessig's campaign may have long since dissipated.

Watch Larry Lessig's interview with Vox's Ezra Klein: