Obama used a recess appointment to name former Ohio Attorney General Richard Cordray as the head of the new agency, which is aimed at imposing new rules on banks and financial institutions to make their dealings with customers more transparent.
The CFPB has been the bane of many conservatives who say it will stifle the financial industry by imposing unwarranted regulations. Blunt, a Republican, voted against Cordray's nomination last month saying the newly created position he will occupy has too much unchecked authority.
"President Obama's latest power grab is unprecedented and raises serious constitutional questions," Blunt said in a written statement. "By using a recess appointment to circumvent Congress, the President is attempting to circumvent the U.S. Senate's constitutional responsibilities in order to enact another unaccountable czar with unlimited power."
Although the president's power to make recess appointments was originally written into the constitution only as a means for the chief executive to fill emergency vacancies while the Congress was out of session, in modern times both Republican and Democratic presidents have used it to perform an end run around hostile legislatures.
Obama also used recess appointments to fill three vacancies on the National Labor Relations Board on Wednesday.