On top of the more than half a million dollars it spends on speechwriters, the White House is using tens of thousands of taxpayer dollars on a public relations firm headed by Democratic image maker Michael Sheehan — once dubbed by Secretary of State Hillary Rodham Clinton as an “extraordinary media coach” who helped her master the teleprompter. Mr. Sheehan’s firm, Sheehan Associates, could receive more than $100,000 under a current contract and has been providing occasional speech and consulting services to the White House since 2009, federal purchasing records show.