Lee Drutman, a senior fellow in the program on political reform at the Washington-based think tank New America, is the author of " The Business of America is Lobbying " (Oxford University Press, March 2015). The opinions expressed in this commentary are his.

(CNN) Harvard law professor Lawrence Lessig announced Tuesday that he is exploring a run in the 2016 presidential election. He intends to put the pressure on Democrats to make fundamental changes to our electoral system, most significantly on the topic of campaign finance reform , by running as a "referendum candidate." But if he wants to make a difference in getting his agenda passed, he's making a mistake in running as a Democrat. He should consider running as a Republican.

Lessig's instincts about how to make a difference on a single issue are right: Because the media covers the presidential race in jarring disproportion to anything else in our politics (like, say, actual governing), a great way to get attention for an issue is to grab the megaphone that comes with running for president.

We wouldn't even be talking about Lessig today if he had simply announced his Citizen Equality Act of 2017 untethered to a presidential run.

However, to really move the debate forward on campaign finance reform, he should run as a Republican, not as a Democrat. The problem is not that Democrats are abandoning campaign finance reform issues (They are not). The problem is that Republicans are ignoring the issue pretty much altogether (absent the notable exception of Trump claiming to have bought off all his Republican rivals).

Among the Democrats, Bernie Sanders has come out strongly for publicly funded elections. And Hillary Clinton may as well.

Certainly, one can accuse Democrats of supporting reform in principle while taking large sums of money from wealthy donors in practice. But I'm sympathetic to the view that these are the rules of the game, and you have to win the game to change the rules. Lessig himself urged supporters of his Mayday PAC to "embrace the irony" in getting rich donors to spend big money to get big money out of politics.

While campaign reform used to have bipartisan support, with prominent backers including John McCain and Barry Goldwater, today the main obstacle is uniform Republican opposition, particularly in the Senate, and even to uncontroversial reforms such as improved transparency.

For a moment, let's assume the unlikely: That Lessig somehow actually succeeds in getting Hillary Clinton to promise make his democracy agenda her top priority. Hillary Clinton campaigns on it as a central plank. Republicans are almost certain to hold control of the House.

Will House Republicans as much as pass such legislation out of committee? Unlikely.

Will Senate Republicans, led by that passionate defender of unlimited campaign spending, Mitch McConnell, reverse decades of opposition and come out in support? Even more unlikely.

If Democrats had majorities in the House and the Senate, there's a decent chance they would pass something like Sarbanes' Government by the People Act, which would create a small-donor matching system. But they are not in control.

Meanwhile, Republicans in Washington are dead set against campaign finance reform. However, what's notable is that Republicans not in Washington hate the current campaign finance system almost as much as Democrats. In poll after poll, large majorities of Republicans also complain our system is broken.

For example, a recent New York Times poll asked people the following question: "Thinking about the role of money in American political campaigns today, do you think money has too much influence, too little influence or is it about right?" 80% of Republicans (and 84% of all respondents) said "Too much." These kinds of results are consistent across most polls.

What if somebody gave voice to those complaints? As Lessig himself said in his Tuesday news conference, "Ideally, there should be a referendum candidate on the Republican side."

Earlier in the Republican presidential primary, a few candidates started to make some noises about the campaign finance issue. Back in April, for example, Lindsey Graham said, "You're going to have money dumped in this election cycle that's going to turn off the American people. There's going to be a need and a movement to try to control the money in politics." But now that they've all taken to begging billionaires for bucks, those noises have grown quiet.

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Sure, Lessig has mostly been hanging out with Democrats of late. But he clerked for conservative stalwarts Justice Antonin Scalia and Judge Richard Posner. In his book, "Republic, Lost: How Money Corrupts Congress -- and a Plan to Stop It," he reveals that he was also once the Pennsylvania state chairman of the Teen Age Republicans. Donald Trump apparently used to hang around with Democrats , too, and that hasn't hurt him.

By associating himself so strongly with a set of issues, Lessig runs the risk of marginalizing those issues if he does poorly. If he polls at, say, 4% as a Democrat, it will be a sign that Clinton doesn't need to take him or his issues seriously.

By contrast, if he polls like that as a Republican, he's in the Top 10. He's on the debate stage, where he gets a few minutes to raise issues of money in politics, and maybe push some Republicans into addressing fundamental issues of campaign finance and participation. After all, remember that Teddy Roosevelt, a Republican, was a leading crusader against excessive money in politics. In 1907, he got a law passed that bans corporations from giving directly to candidates, a ban that is still in effect today.

I agree with Lessig that our political process is flawed, that it gives disproportionate influence to a small slice of very wealthy people, and that we ought to do something about this (though I'd put more emphasis on the way in which the tremendous imbalance in lobbying resources changes how the legislative process works, even absent campaign finance pressures). I hope Lessig's jump into the 2016 election amplifies these concerns.

But the deeper problem is that campaign finance reform has become a partisan issue in Washington. If Lessig really wants to make a difference, he should be putting the pressure on Republicans, not Democrats. It's the Republicans who have made progress impossible.