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It is unclear what action Paul is suggesting, although he has previously said that Obama could be impeached for other actions the Texas congressman described as unconstitutional, including the drone killing of terrorist leader Anwar al-Awlaki, who was an American citizen, and the president's decision to undertake military action in Libya without congressional approval.

President Obama made the appointments Wednesday despite Republicans in the Senate holding "pro forma" sessions every few days to prevent a technical recess. The GOP was hoping to cripple the agencies, unpopular in conservative circles, by refusing to confirm the appointments. Republican lawmakers wanted changes to the CFPB including a multimember board to run the bureau instead of a single director.

Obama defended his recess appointments in a speech in Ohio on Wednesday.

"When Congress refuses to act and as a result hurts our economy and puts people at risk, I have an obligation as president to do what I can without them," Obama said. "I have an obligation to act on behalf of the American people."

But Paul blasted Obama's actions as "in clear disregard for the Constitution."

“It is disappointing that a former constitutional law professor does not understand that the President is not a dictator or a king who can simply ignore the Constitution whenever he feels frustrated by the system of checks and balances wisely put in place by our Founders," Paul added, saying the president "must be called to account for his actions."

On Wednesday, Rick Santorum — one of Paul's opponents for the GOP nomination — suggested the Senate should sue over Obama's move.