There’s an important cliche regarding history that Obama appears to know nothing about: those who ignore history are bound to repeat it. By taking on Rush and making him the target, Obama is expanding Rush’s reach and influence. He is making Clinton’s mistake:

By one measure, Rush Limbaugh is a clear winner this week: His ratings have nearly doubled since his feud with the White House burst into the media limelight.
[…]
This is not the first time Limbaugh has bedeviled a Democratic president. In 1994, Bill Clinton lashed out at conservative talk show hosts, saying that Limbaugh “has three hours to say whatever he wants” with “no truth detector.” Limbaugh helped galvanize support for the Republican takeover of Congress that year.

I’m not sure it’s in the best interest of the president to send listeners to hear of all his missteps, lies, and total lack of understanding of what to do when in a recession (i.e., cut corporate and capital gains taxes — even China get’s it). Limbaugh can be very persuasive:

But, McKinnon said, “whatever you think of Rush, he is one of the most effective political communicators in history. So I don’t think turning up his microphone is necessarily a wise way to go.” For Obama, he said, “a fistfight with a brawler like Rush only drags him down to the street.”