I didn't bring a bag/backpack in 2006 and I don't remember if I brought bottled water into the stadium... of course, after tailgating for 6 hours, it's really hard to remember anything except that TEXAS WON!!!!
Their website says no backpacks, but they will have a bag check at the stadium. It also says that sealed plastic bottle smaller than 2 liters may be brought in.
That was most lax, jaw-dropping security I've ever seen at a very major sporting event. We walked right in with a backpack and huge binocular case, and no one even stopped up. It was incredibly terrible security, but it made it easy getting our 2 pints of bourbon in.