Theodore Roosevelt IV, a member of the group and the great-grandson of President Teddy Roosevelt, said the measure aims would put power back in the hands of voters.
"It is unconscionable, in our society, that Congress is held in such low esteem," he said. "[It is] materially important to re-establish the sovereignty of the American people."
Board members for Represent.US say they are developing a plan to challenge lawmakers who refuse to endorse their bill.
The organization, which is operates two non-profits, will accept donations to pursue its agenda — all of which will be fully disclosed.
Campaign finance reform has faced opposition in Congress since the McCain-Feingold bill was approved in 2002. Represent.US members said they will reach out to reform opponents, particularly in the GOP.
Richard Painter, former chief ethics advisor to President George W. Bush, said he will be a voice to "persuade my fellow Republicans to back campaign finance reform."
The group's leadership also includes a head of the DC Tea Party Patriots, a Harvard Law School professor and disclosure advocate, a former senior Democratic congressional staffer and a Republican strategist.