From The American Political Dictionary
gotcha question /'ga-cha kwes-chen/: a question asked by an interviewer of a candidate who has no idea how to answer it, and is offended that someone should have the effrontery to ask a question about foreign or domestic policy of a candidate who is running for the highest office in the land.
Etymology: The phrase was popularized by Sarah Palin, a candidate who in 2008 was running for the second highest office in the land and, concerning questions of policy, didn't know her ass from a hole in the ground.