Committee leaders push the NCUA and CFPB to cease any involvement with the operation.
Texas Congressman says CFPB should choose a less costly alternative such as selling the building to the highest bidder.
Report details three key areas the bureau must improve.
Incoming NCUA Board Member J. Mark McWatters also touts transparency and cost-benefit analysis for rulemaking.
The House Financial Services Chairman asks the NCUA to explain how examiners use reputation risk to judge safety and soundness.
"While there has been substantial job creation, we have further to go," new Fed chairwoman tells House Financial Services Committee.
The Republican-led House Financial Services Committee grilled the CFPB director on building renovations.
Republican-led House Financial Services Committee launches site one day before CFPB Director Cordray presents semi-annual report.
House Financial Services spokesman said committee would examine data security, but would not answer specific questions about Target.
Texas Republican, who served on the Congressional TARP Oversight Panel, would replace Board Member Michael Fryzel.