WASHINGTON — The petitions that started surfacing online over a year ago were as incendiary as they were urgent, begging recipients to sign up to “Boot Boehner,” “Dump McConnell,” “Drop a Truth-Bomb on Kevin McCarthy” and “Fire Paul Ryan.”

The calls to oust Republican leaders in Congress did not come from Democrats. They came from conservative websites and bloggers who have helped stoke a grass-roots rebellion to make Congress more conservative, a fevered continuation of the six-year Tea Party movement.

But these politically charged appeals to conservatives around the country were often accompanied by a solicitation for money, and the ultimate beneficiaries, records suggest, are the consultants who created the campaigns rather than the causes they are promoting.

It is a practice that has accelerated with the explosion of social media. The latest example came on Wednesday with a new attack on Representative Paul D. Ryan, Republican of Wisconsin, just a day after he said he was willing to serve as House speaker.