Lynn Sweet of the Sun-Times reports on why President Obama is going on Jay Leno Thursday night:

WASHINGTON–President Obama sits down with Jay Leno on Thursday, while in California to sell his stimulus and budget plans and the path for long term economic growth. At the Tuesday briefing, White House spokesman Robert Gibbs said Obama is going on the late night show to talk about his economic plans.
While Obama will be doing two town halls in California–a state struggling with high unemployment and a state government funding crisis–Leno provides a “unique” audience, Gibbs said.
“We don’t look at it as a process of demonstrating the president’s sense of humor,” Gibbs said, but rather a chance “to explain the economic situation we are in.”

Another reason might be that there probably is not another voice in the media more supportive of the Big Three than car buff Jay Leno. I imagine there will be a cupcake question or two on the auto industry that will allow President Obama to explain how he’s doing the right thing with the Detroit bailouts.