Cordray has been rumored to be considering a candidacy for governor of his home state of Ohio in 2018.

House Financial Services Chairman Jeb Hensarling (R-Texas) told Cordray during a hearing earlier this year that President Trump should fire him.

Hensarling did not mince words, in discussing Cordray's resignation Wednesday.

“We are long overdue for new leadership at the CFPB, a rogue agency that has done more to hurt consumers than help them,” he said. “The CFPB tramples on the fundamental economic rights of American citizens, taking away their choices and opportunities.”

Credit unions have said that all too frequently, the CFPB has not differentiated between big banks that were the cause of the financial crisis and credit unions, which did not cause the crisis.

“We continue to believe that credit unions should never have been lumped into the same regulatory bucket as the big banks and look forward to continuing to work with new leadership to address credit union issues,” said NAFCU President/CEO Dan Berger said, following Cordray's announcement.

CUNA/President CEO Jim Nussle had a similar reaction to the news.

“Moving forward, CUNA urges the CFPB's new leadership to address the problems that pending and final rules have caused credit unions and their 110 million members, and move towards a new approach that recognizes the exceptional consumer protections credit unions provide, while continuing to address abusers of consumers,” he said.

However, supporters of the agency have pointed to agency enforcement actions that have resulted in $12 billion being returned to almost 30 million consumers.

The status of the CFPB director is hung up in federal court. A panel of the U.S. Court of Appeals for the District of Columbia has ruled that the makeup of the agency is unconstitutional, since it is run by a single director, which only can be removed for cause.

However, the agency has appealed that ruling to the full D.C. Court of Appeals, which has heard arguments in the case, but has not issued a ruling.

In addition, the confirmation of a new director is likely to result in a political battle between president Trump and the Senate.

A White House spokesperson said that Trump will select an interim CFPB head and then nominate someone later. The interim head could be someone like Treasury Secretary Steven Mnuchin, who then would delegate the duties to a subordinate.

Trump is likely to want a candidate that is friendlier to business than Cordray has been.

On the other hand, the agency does have political support among Democrats and some Republicans.

That strength was evident recently, when the Senate voted to nullify the CFPB's arbitration rules. It took a vote by Vice President Pence to break a 50-50 tie to rescind those rules.

Senate Banking ranking Democrat Sherrod Brown of Ohio gave a preview of that upcoming battle in reacting to Cordray's resignation.

“The White House has said it wants to stand up for the middle class,” he said. “If that's true, the President must nominate a successor who will put working people ahead of Wall Street.”

Sen. Elizabeth Warren (D-Mass.) sounded a similar theme

“The new Director of the [agency] must be someone with a track record of protecting consumers and holding financial firms responsible when they cheat people,” she said. “This is no place for another Trump-appointed industry hack.”