WASHINGTON — As tension built in the House of Representatives in recent weeks, it was sometimes hard to know whom hard-line conservatives were gunning for more: President Obama or their own Republican speaker, John A. Boehner.

As it turns out, their target is the institution of the speaker of the House itself.

To get to the broader goal of confronting Mr. Obama, they want to alter the fundamental power structure of the House by reducing the power of the speaker in favor of greater authority for the rank and file.

“I want to see a change in the culture of Washington D.C.,” said Representative Barry Loudermilk, a freshman from Georgia who is a member of the Freedom Caucus that helped drive Mr. Boehner from office. “The way you do that is not who you elect, but it’s the process. It’s the procedures.”

“How are we going to change the process, how are we going to make it a more bottom-up versus a top-down structure?” he said.