Republicans haven’t minced their words on the campaign trail about President Obama’s recess appointment of Richard Cordray to head the Consumer Financial Protection Bureau. Newt Gingrich accused Obama of having “a total willingness to violate the law and impose an imperial presidency." Mitch McConnell, the Senate’s senior Republican, said that Obama “arrogantly circumvented the American people.”

The flap over the controversial appointment has blown over by now—at least until the courts take up its legality, considering the Senate was technically in a pro forma session specifically to stop Obama appointments. But that hasn’t stopped the candidates from hammering away at the CFPB itself on the campaign trail.

The question is: have they been honest in their critiques of the agency designed to protect consumers who apply for mortgages or take out other loans?

Not quite. Exhibit A might be Rick Santorum, the surprise Iowa second placer, desperately trying to finish strong in New Hampshire on Tuesday. While campaigning in the Granite State over the weekend, Santorum painted a dark picture of the new bureau. The CFPB is “a pretty scary thing,” he said. It can determine “what loans you’re going to be able to qualify for, who you can do business with.” He ended his tear by accusing the Obama administration of regarding people in business as “nefarious” by nature.

That’s simply not true. The budding agency, finally in operation following Cordray’s appointment, was created by Congress to crack down on banks, credit-card companies, foreclosure officers, and debt collectors who are accused of taking advantage of consumers. By design, it’ll work with individuals who have complaints about financial institutions, but it won’t regulate the choices people make about their finances. Created under the Dodd-Frank financial reform bill in 2010, the CFPB has never caught favor from Republicans. After unsuccessfully trying to block Cordray’s appointment, senior Republicans have now threatened to sue the White House and block the bureau’s funding—one of Congress’s few authorities over the executive agency.

Cordray, through a spokesperson, declined to respond directly to Santorum, keeping with the White House’s MO of staying out of the GOP fray until the president has a specific challenger to face. But in a private conversation, the White House bristled at Santorum’s suggestion; an aide said Santorum was simply trying to drum up fear by spreading untruths.

Cordray, meanwhile, has made the rounds of Washington to combat such rhetoric. “Our work will support the honest businesses in financial markets against those who deceive consumers or otherwise break the law,” Cordray said last week at the Brookings Institution, a Washington think tank. “We are confident that if the public understands our job, they will help us play our important role in safeguarding consumers as well as the broader American economy.”

Other candidates have also tried to lump CFPB and Cordray into their campaign narrative that Obama is overreaching. Mitt Romney called it “the most powerful and unaccountable bureaucracy in the history of our nation,” referring to the unprecedented autonomy the bureau will have from meddling by Congress. Jon Huntsman simply referred to the agency as an “unguided regulatory missile” that will limit free commerce.

The White House is confident it can win the argument over CFPB. Obama’s Chicago campaign has said that it’s extremely helpful for Republicans to so adamantly oppose efforts to protect consumers against things as disagreeable as predatory lending and interest-rate deception. As Obama twists himself into a pretzel trying to explain the economy’s sluggishness on his watch, the argument over the value of the CFPB, one campaign insider says, is one he doesn’t mind having.