No Power in Passing Gear

OK...Came into work tonight and tried passing a car on the way in...when I pushed the gas pedal down you could hear the transmission spin up but there was no power. The vehicle maintained it's current speed but would not shift into passing gear. If I slowly eased into the gas pedal I would get power and it drove fine. It was just when I pushed the gas pedal all the way down. I have a 97 GMC K1500 with the 350 Vortec. I'm not real knowledgeable about engines, transmissions or anything else under the hood aside from pointing out what some of the obvious stuff is. Anyone else experience any similar problems or have any advice how to resolve this? Any feedback would certainly be appreciated. BTW...this happens whether I'm level, uphill or downhill.