Here's the long version (24 min) from the Obama Campaign site. You might want to skip to the 14 min mark or so for a reasonable lead in.
So why would we need a "civilian national security force that is just as powerful, just as strong, and just as well-funded" as the military? We already have the Army, Navy, Air Force, Marines, National Guard, TSA and various federal and state law enforcement agencies. Since Defense is about 20% of regular federal spending (whatever that means these days), this suggests a massive spending project without any apparent purpose.
Taking the relatively benign interpretation of Obama's proposal, he may be suggesting, as the Left is wont to do, that all desired spending is a matter of "national security." He doesn't really have anything useful for them to do, but he's sure it needs to be done in a big way. In this interpretation the plan is only a colossal waste of money, to be spent on make-work projects like the FDR administration promulgated during the Great Depression. These kinds of programs were ineffective then, and they might well precipitate a depression if tried now.
Looking beyond that, we can guess that this may be a vehicle for channeling more federal money into favored "community organizations" such as ACORN, Nation of Islam, etc. Such a powerful, strong, well-funded civilian force would be very handy to have in the future for stealing elections, intimidating opponents, and perhaps busting a few heads, as needed. Anyone for pogroms?