Portman, who was one of 17 GOP senators to support Cordray in a cloture vote, said it makes sense to ensure that the agency is transparent in its work.
"Given the important role we’ve seen an IG play in the IRS scandal, creating an independent IG dedicated to this large bureaucracy with vast powers is a common-sense step we can take to ensure greater transparency and accountability at the CFPB," he said.
Despite losing the leverage of holding up Cordray — Democrats had dug in against the push to create a bipartisan commission to head the agency — the Senate GOP is expected to continue pushing for changes for the agency, which was created by the Dodd-Frank financial law in 2010.
Republicans have argued that, while they like Cordray and think he is doing a good job, the volume of the agency's work — from mortgage rules to monitoring credit card company practices — is too much for one director.
The Senate voted 71-29 to end a GOP filibuster of Cordray, which ran for more than 700 days.
A final vote on Cordray's nomination to serve a five-year term will happen on Wednesday.
The vote came as part of a broader deal on a set of stalled nominees meant to avert the nuclear option, which Senate Majority Leader Harry ReidHarry Mason ReidDemocrats say Biden must get more involved in budget fight Biden looks to climate to sell economic agenda Justice Breyer issues warning on remaking Supreme Court: 'What goes around comes around' MORE (D-Nev.) said he would use if the GOP refused to agree to the up-or-down votes on seven nominations.