He noted emails that have emerged that say Chu "may have to go."
Barton didn't provide specifics, but may have been referring to an email that a former Obama administration campaign aide sent to senior White House officials earlier this year. The email from Dan Carol, a green-energy expert, called for Chu to be replaced as secretary as part of a broader set of changes at the Department of Energy that Carol recommended.
Pete Rouse, a top White House aide, brushed off the criticism of Chu in an email made public earlier this month while asking colleagues for input on Carol's other views.
Barton spoke during Chu's appearance before the House Energy and Commerce Committee investigative panel, which is probing the $535 million loan guarantee to Solyndra in 2009. The company went bankrupt in early September.
Barton did, however, say Chu is "culpable" for the decision to restructure Solyndra's loan early this year. The restructuring put private investors — who agreed to inject more money into the struggling company — ahead of taxpayers for repayment if Solyndra liquidated.
Rep. Steve Scalise (R-La.), another member of the committee, echoed Barton's concerns, arguing that the White House could make Chu a "scapegoat" for the handling of the loan guarantee.
"Just to throw one person under the bus just to end this investigation, that’s not, I don’t think, in the best interest of transparency," Scalise said.
"The administration is looking for any kind of scapegoat they can to throw under the bus to try to end this investigation," Scalise continued. "But we’re going to take this as far as the facts will lead us."
Scalise called on the Justice Department to launch an investigation of the Energy Department's February decision to restructure the Solyndra loan. Republicans have alleged that the decision to "subordinate" the interests of the taxpayer to those of private investors violates the law.
"I think we need to challenge the subordination of the taxpayer because I think it was illegal. And then hopefully we can reverse that so the taxpayers will have some opportunity to get reimbursed," Scalise said. "I think it’s time that the Department of Justice does their job and goes and looks about whether or not the law was violated."
This post was updated at 3:59 p.m.