A funny thing’s happening on the way to Nov. 6. The billionaires trying to buy the U.S. election with contributions of $1 million, $10 million or even $100 million aren’t succeeding.

If trends continue and the Democrats have a good year (still a big if), the notion that in order to win candidates must accept gobs of money from super-political action committees will be discredited.

Then we’ll see a small opening for a practical solution to our corrupt politics that would require no spending limits, no barring of super-PACs and no constitutional amendment to overturn the Supreme Court’s Citizens United decision.

This solution would free at least some candidates for federal office from dispiriting and corrupting lives of endless fundraising and legalized bribery. It would strike a blow for democracy, localism and choice (always a crowd-pleaser for the Republicans) in our elections.

It’s important to understand why the deluge of super-PAC contributions — and those from shadowy 501(c)4 groups, which don’t require disclosure — isn’t working as well as Republican strategists Karl Rove and the Koch brothers or the casino billionaire Sheldon Adelson may have hoped. (The same goes for the relative pikers on President Barack Obama’s side, such as the Priorities USA super-PAC).

The reason is that big money in politics has a competitor: small money in politics. Even though big money is winning this year — it accounts for more than 75 percent of donations — small money raised on the Internet is better adapted to the 21st century political battlefield.

Big money is used mostly to pay for negative television ads. These spots can still be potent and force the other side to raise enough money to rebut them. But Americans, especially younger voters, aren’t watching TV the way they used to. They’re time-shifting programming and are increasingly cynical about ads. With all the airwave pollution, saturation levels are reached earlier, especially if the messages in the ads are at odds with what’s going on in the news.

Mitt Romney, the Republican presidential nominee, and several trailing Republican Senate candidates are finding this out.

Super-PACs can dominate the air war, but they have trouble buying ground troops. Political strategists know from experience that phone banks and canvass teams made up of low-wage hired help are far inferior to those using volunteers sincerely trying to persuade voters.

The reason the Obama campaign sends out so many irritating requests for $3 or $5 donations is that these solicitations do more than just raise cash. Once millions of small donors have a little skin in the game, they’re much more likely to assist with registration and get-out-the-vote efforts. This willingness to help can’t be purchased by super-PACs at any price.

I’m not suggesting that small donations are competitive yet. In House races in 2010, only 8 percent of contributions were for less than $200. But with a boost, small money can play with the big boys.

In “Empowering Small Donations in Federal Elections,” Adam Skaggs, of the Brennan Center for Justice, and Fred Wertheimer, the founder and director of Democracy 21, offer a voluntary plan based on the very successful model adopted in New York City. Contributions of $250 or less would be matched by federal funds at a 5-to-1 ratio. Thus, $250 would yield $1,250, which would be the upper limit on allowable contributions for the candidates who participate. (That cap might be too low, but let’s not quibble.)

The system would require a certain threshold of in-state donations to encourage local participation and would be capped at $2 million for a House campaign and $10 million for a Senate race. The total price — $700 million a year — is an enormous bargain for taxpayers because the changes would help prevent big donors from buying tens of billions in tax breaks, subsidies and other favors. If the Republican Party is serious about removing the special-interest breaks that would be necessary to achieve comprehensive tax reform, it will need to be shielded by matched financing of elections.

Candidates who opt out could continue to operate under the old system, as did Mayor Michael Bloomberg in New York (the founder and majority owner of Bloomberg News parent Bloomberg LP). But there might be a political penalty to pay for those who go it alone. In Massachusetts this year, both Senate candidates, the incumbent Republican Scott Brown and his Democratic challenger Elizabeth Warren, agreed to keep super-PAC money from soiling their race.

Lest you think that federal legislation is a pipe dream, consider that public financing of general elections was accepted by all major party presidential nominees from 1976 until 2008, when Obama opted out after the outdated dollar limits in the matching funds turned out to be lower than the amounts he was raising on his own. This places a special responsibility on the president to help restore a system he helped destroy.

So far, 15 states and several cities have public financing systems, some more effective than others. Republicans, who are often philosophically opposed to this idea, have been especially big supporters of its application in Connecticut, where Republican Governor Jodi Rell was elected in 2006 with small- donor contributions, and in Arizona, where Tea Party candidates used the public financing system to unseat establishment Republican primary candidates. When their interests matched, Tea Party types forgot their ideological objections, just as they have in supporting Medicare. This might offer some hope of getting a bill through Congress.

Small-donor reform also loosens the grip of corporations and unions. Romney was right when he said this week that “we simply can’t have a setup where the teachers unions can contribute tens of millions of dollars to the campaigns of politicians and then those politicians, when elected, stand across from them at the bargaining table, supposedly to represent the interests of the kids.”

Then there’s the wasted time for politicians. Because Romney is so reliant on big donors, he has to spend precious hours at high-end fundraisers instead of campaigning among all voters. The now-infamous video of him dissing the “47 percent” might have taught him the dangers of the system. Obama, too, is distracted by having to show up at dozens of fundraisers. In 1984, President Ronald Reagan tapped public financing and attended none.

Finally, the do-gooders have to stop calling this “campaign finance reform” or “public financing.” That’s bad branding. Next year, after the fiscal cliff is avoided, the hard work of building a movement for small-donor reform will have to begin. Power to the pea shooters.

(Jonathan Alter is a Bloomberg View columnist and the author of “The Promise: President Obama, Year One.” The opinions expressed are his own.)

Photo by “401(K) 2012” via Flickr.com