It won't be able to coordinate directly with parties or political entities, but as similar nonprofits, like Crossroads GPS and Americans for Prosperity, showed during the 2012 elections, these groups can still be formidable political forces.

According to a tally from the Sunlight Foundation during the week prior to the election, outside groups with a similar structure to OFA spent more than $213 million on the general election this past cycle.

Democracy 21 works against the influence of outside money in politics, and Wertheimer warned that the shift in OFA's purpose is "fraught with danger."

"It opens the door to opportunities for government corruption, by allowing corporations and individuals to provide unlimited amounts of money to directly benefit the President’s interests and potentially to receive government benefits and favors in return," he wrote.

Wertheimer added: "This action by the President also represents the last stage in an apparent remarkable transformation in President Obama’s views regarding the role of corporate money in the American political process."

When the Supreme Court finalized the decision in the Citizens United case that created super-PACs and opened up new opportunities for outside money to influence politics, Obama roundly criticized the court, accusing it of giving "a green light to a new stampede of special interest money in our politics."

Wertheimer turned Obama's words back around him, accusing him of doing the same thing by condoning, and perhaps aiding, the new group.

"This would take President Obama about as far away as he could possibly get from the goal he set in 2008 to 'change the way business is done in Washington,' " Wertheimer charges.

The organizers of the new group have pledged to disclose its donors, and not take money from political action committees or lobbyists, but Wertheimer expressed skepticism that OFA would stick to its word. And if Obama doesn't heed the group's warning and dismantle OFA, Wertheimer pledged that Democracy 21 "will closely monitor its activities."