Read through the entire Edmunds web site to get the whole story. It's all there if you want to read.
Right now with the employee discounts and rebates going on you are not going to get much lower, the price you will be paying will be less than the TMV. I have a friend that tracks prices closely - he's one of those types that buys a new truck, then trades it it for another less than a year later. I think he's been through about 3 Silverados in the last 2 years. He talked me into going Silverado shopping a few weeks ago - I ended up with a 2005 Dark Metallic Blue 4WD Silverado LS Crew Cab with the chrome step ups, 17" aluminum wheels, towing package, power folding mirrors, power driver seat, deep tinted glass, skid plates, 4.10 rear axle ratio... for about 27g's after the $3,000 rebate and before taxes. I don't even see some of the options on Edmunds, but if I take the TMV of the options they do list and add the other options I received the TMV on Edmunds would be about $29,500 including the rebate.
I think I payed about $2,500 less than the TMV on Edmunds when I bought our 2004 Honda Odyssey a few years back also.
So, yes - you should shoot for less than the TMV and there is no haggling involved right now with the employee discounts.