“Unless the bureau is reformed,” said Senator Richard Shelby, the Alabama Republican who is the committee’s ranking minority member, “it is only a matter of time before this concentration of power is abused or misused to the detriment of American consumers and the economy.”

Mr. Shelby and 43 other Republican senators have vowed not to allow a vote on a nominee for director unless the Obama administration agrees to changes in the bureau’s structure. In a letter to Mr. Obama in May, the senators called for a board of directors to replace the position of director, for subjecting the bureau to the Congressional appropriations process, and for putting in place guarantees that enforcement of consumer regulations will not interfere with the financial health of banks.

Senator Robert Corker, Republican of Tennessee, assailed committee Democrats for “spewing” what he said were “half truths, mistruths, untruths” about the effort to build the consumer agency. “Almost all of this would go away if the administration would just sit down and put the appropriate checks and balances in place,” including making it easier to override regulations approved by the bureau, Mr. Corker said.

Such regulations can be overturned by a two-thirds vote of the 10-member Financial Stability Oversight Council, which includes the directors of most federal banking and financial regulatory agencies. But Mr. Shelby and other Republicans have argued that that was too high a hurdle and meant that council’s authority rarely be invoked.

Mr. Cordray acknowledged that it was a high hurdle, but one that should not need to be invoked. “We are required by law to communicate and consult with our fellow banking agencies,” he said. “I would hope and expect that concerns that they have about our work and concerns we may have about their work are things we will discuss regularly, that we will work those issues out when we do have disagreements, as I’m sure will occur from time to time, and that it never be necessary to actually invoke some sort of super process to override our rules.”