WASHINGTON — House Republicans on Friday replaced the firm handling their lawsuit against President Obama after the lawyer representing them pulled out over what was said to be political backlash among his colleagues at the firm, Baker Hostetler.

The lawyer, David B. Rivkin Jr., had taken the case on behalf of House Republicans in August, right after they voted to sue the president, accusing him of overstepping the powers of the presidency. Two people with knowledge of the situation said Mr. Rivkin withdrew from the case under pressure after facing criticism that he had taken on an overly partisan lawsuit. Some members of the firm feared the case against Mr. Obama could drive off potential clients and hurt Baker Hostetler’s credibility, according to one of the people with knowledge of the case. Both people said they were prohibited from publicly discussing such a delicate case.

With Mr. Rivkin’s withdrawal, the House Administration Committee signed a new contract on Friday with William A. Burck, co-head of the Washington office of Quinn Emanuel Urquhart & Sullivan. Mr. Burck had served as outside counsel for the House Committee on Oversight and Government Reform when House Republicans sued Attorney General Eric H. Holder Jr. to produce documents related to the botched gunrunning investigation known as Operation Fast and Furious.

He also represented Maureen McDonnell, the wife of former Gov. Bob McDonnell of Virginia, in the corruption trial that ended this month with her conviction on nine counts.