Obama said Cordray's job is important "because there is an army of lobbyists and lawyers right now working to water down the protections and reforms that we passed."
"They've already spent tens of millions dollars this year to try to weaken the laws that are designed to protect consumers, and they've got allies in Congress who are trying to undo the progress that we made," he said. "We're not going to let that happen."
Obama said that the CFPB consolidates consumer protections, providing consumers with one place to send complaints or ask questions that had previously been spread throughout the federal government.
"We put one consumer watchdog in charge with just one job: watching out for regular people in the financial system," he said.
Senate Republicans on Monday expressed continued opposition to one director heading up the agency.
Senate Minority Leader Mitch McConnellMitch McConnellStudy: Trump tops recent GOP presidents in signing bills in first 100 days Senate passes stopgap funding bill to avert shutdown Let’s never talk about a government shutdown — ever again MORE (R-Ky.) said Senate Republicans "still aren’t interested in approving anyone to the position until the president agrees to make this massive new government bureaucracy more accountable and transparent to the American people."
In May, 44 Senate Republicans sent a letter to Obama saying "we will not support the consideration of any nominee, regardless of party affiliation, to be the CFPB director until the structure is reformed."
“And we’ve been very clear about what those reforms would look like," McConnell said.
“We have no doubt that, without proper oversight, the CFPB will only multiply the kind of countless burdensome regulations that are holding our economy back right now, and that it will have countless unintended consequences for individuals and small businesses that constrict credit, stifle growth, and destroy jobs."
The changes demanded by the GOP include the creation of a five-member commission to oversee the new agency.
"Although this deadline has been known for nearly one year, President Obama waited until the last possible moment to act," said Sen. Richard Shelby (R-Ala.). "For months he has ignored Republican concerns about the lack of accountability at the CFPB and its potential adverse effect on the economy. Until President Obama addresses our concerns by supporting a few reasonable structural changes, we will not confirm anyone to lead it. No accountability, no confirmation."
The U.S. Chamber of Commerce didn't express concern specifically about Cordray, but did criticize the power the agency will provide its director.
"We have deep concerns about how he would use its new broad powers," said David Hirschmann, president and chief executive of the Chamber's Center for Capital Markets Competitiveness.
Hirschmann outlined a few of the areas of concern, notably enforcement settlements in the mortgage industry.
Cordray was one of the first people chosen by Warren to get the agency ready for business. The new bureau opens its doors Thursday, a year after it was created.
Obama credited Warren's work at the newly created bureau, saying she had helped simplify credit card agreements and provided greater protections for veterans against fraud and deception.
He said the financial crisis and the recession weren't the result of "normal economic cycles, or just a run of back luck."
"There were abuses and a lack of smart regulations," he said.
Cordray joined the CFPB in January and heads the agency's enforcement division. After serving as Ohio attorney general for two years, he lost his reelection bid in Nov. 2010. Warren called him in December to take the job as the bureau's enforcement officer.
Cordray became known last year for aggressively investigating big banks with questionable foreclosure practices in Ohio and helping retirees recover billions in pension funds.
Warren expressed support for Cordray's nomination.
"Rich has always had my strong support because he is tough and he is smart — and that's exactly the combination this new agency needs,' Warren said in a statement. "He was one of the first senior leaders I recruited for the agency, and his work and commitment have made it clear that he will make a stellar director."