Hensarling's proposals carry particular weight because he is chairman of the House Financial Services Committee.
Other bills introduced in the Senate recently have also taken aim at the CFPB. Sen. David Perdue, R-Ga., and 11 of his colleagues have proposed subjecting the agency to the appropriations process; the CFPB is currently funded through the Federal Reserve. Another bill from Sen. Ted Cruz, R-Texas, would repeal the agency altogether.
"It was intentionally created to protect it from political interference and the political allies of finance killing it," said Dennis Kelleher, chief executive of Better Markets. "We knew that an effective consumer protection agency would immediately become the number one priority target of finance."
Doing away with the CFPB could prove dicey despite GOP control of Congress.
A D.C. court said Thursday it would give a second look at a lawsuit that argues the agency's structure is unconstitutional. White House attempts to remove the CFPB's current director, Richard Cordray, before his term ends next year are also sure to face legal challenges.
Republicans "have to stop pretending their attacks on Director Cordray and the agency are about anything other than carrying water for big banks, payday lenders and debt collectors," said Sen. Elizabeth Warren, D-Mass., who is credited with setting up the agency.
With consumer advocates in full alarm and the banking industry missing its target, neither side is entirely happy right now in the fight over the CFPB.