WASHINGTON — As a sign of the pride Representative Darrell Issa takes in annoying the Obama administration, consider his account of a recent exchange with Rahm Emanuel, a former congressman and now the White House chief of staff. In describing the episode — a chance encounter outside the House gym — Mr. Issa smirked and raised his middle finger. “That’s the only thing Rahm did when he saw me,” Mr. Issa, a California Republican, boasted in an interview in his House office. He waved the unfriendly digit in the air like a trophy before folding it into a nub (to...