The Mayday PAC’s own funding is a mix of large and small: Silicon Valley luminaries like Reid Hoffman, a co-founder of LinkedIn, and Peter Thiel, a libertarian billionaire, have made big contributions to match Mr. Lessig’s small-donor fund-raising.

In Congress, the allies are urging lawmakers to support legislation like the Government by the People Act, sponsored by Representative John Sarbanes, Democrat of Maryland, and the Citizen Involvement in Campaigns Act, sponsored by Representative Tom Petri, a Wisconsin Republican. Both measures offer tax credits or vouchers to people who make small donations. To win Mayday’s support — or fend off the group’s planned attack ads — candidates need only endorse one of these measures.

The limited requirements for the super PAC’s support are intended, in part, to help Mayday enlist more Republicans. Party leaders like Senator Mitch McConnell and conservative legal scholars are deeply opposed to proposals that would diminish money in campaigns, arguing that they are an infringement on free speech and healthy political competition. Mr. Rubens, for example, is in favor of giving voting-age citizens a $50 tax rebate check every two years to be spent on candidate contributions.

“As long as campaign finance is seen as a liberals-only issue, I don’t think we’ll be able to bring in the resources that we need to win,” said Nick Penniman, the executive director of Fund for the Republic, which has received money from members of the Democracy Alliance, a club of top liberal donors. “If you’re a Republican or an independent in this country and you think that money plays too much of a role in politics, you really have no home.”

Mayday’s founders believe that rank-and-file Republicans are more open to limiting the impact of big contributions than their leaders are. Mr. McKinnon worked with Juleanna Glover, a Republican lobbyist and former George W. Bush aide, and Trevor Potter, a Republican lawyer who founded the Campaign Legal Center, to interview 60 Republican and conservative leaders, strategists and activists for their views on money and politics.

They found that Mr. Obama’s ability to outraise Republican presidential candidates in two straight elections had cut against a common belief in Republican circles that unlimited campaign fund-raising and spending gave their party an advantage. At the same time, some of the respondents told them that Republicans’ support for unrestrained campaign money was cementing public suspicion that the party catered to the wealthy.