Obama was not in office in 2008 so the first rating drop is not his fault. This one however is, as it reflects that his policies, and that of congress (which includes Republicans), have not done enough to curb economic decline.
The stimulus package was suppose to prevent unemployment from reaching 8%; it has been higher than that for 40 straight months. People are being hired, but not at a rate to officially call it a recovery.
Obama walked into a bad situation when he came in office and IMO has been a disappointment economically to date. He did not start the fire but he has done nothing but toss more lighter fluid on it.