But her aggressive efforts have angered some Republicans, who charged that an F.E.C. hearing she scheduled for next week on challenges facing women in politics was not only outside the commission’s jurisdiction but a thinly veiled attempt to help the presidential bid of Hillary Rodham Clinton. Ms. Ravel called the accusations “crazy.”

Some disputes between the commissioners have gotten personal.

A disagreement over how to treat online political ads, for instance, turned tense when Ms. Ravel received anonymous online threats over charges that she was trying to “regulate” the Internet. She angrily confronted Mr. Goodman, charging that he had unfairly “fanned the flames” against her by mischaracterizing her position in an interview he did on Fox News. But Mr. Goodman said he had no regrets about challenging her position, which he saw as opening the door to greater regulation of Internet activities.

Relations between the two have been difficult ever since.

Last fall, Ms. Ravel did join Republicans on the commission — and took some criticism from the left — in a 4-to-2 decision that eased rules growing out of the Citizens United decision and a related case. But she has had little success in persuading Republicans to vote with her on enforcement measures.

She said she was particularly frustrated that Republican commissioners would not support cases against four nonprofit groups — including Crossroads GPS, founded by Karl Rove — accused of improperly using their tax-exempt status for massive and well-financed political campaigns.

A surge in this so-called “dark money” in politics — hundreds of millions of dollars raised by nonprofits, trade associations and other groups that can keep their donations secret — has alarmed campaign-finance reformers who are pushing to make such funding public.

But Mr. Goodman said the problem was exaggerated. He and other Republicans defend their decisions to block many investigations, saying Democrats have pushed cases beyond what the law allows.