Assuming that the condition is new, and hasn't been an issue before, and that the problem isn't with a new and improperly installed headset...then I'd say:
Inexpensive cup and ball headsets can easily become 'indexed'. This is a condition where running a dirty or misadjusted headset, or having a headset damaged while riding or in an accident, causes the bearings to wear into a common grove, or force the surface of the cup to deform in such a slight fashion as to not be seen with the naked eye. The most common position for adjusting the slop from a headset is with the bars and fork straight ahead, where the adjustment takes the play out of the worn or damaged part of the cup. Then when you turn the bars, you introduce the bearings back into a section of the cup where the original tolerances still apply, and the headset feels tight.
Solution is either a new headset, or to go the budget route, punch out your cups and turn them 90 degrees in opposite directions. Mark the front of both the top and bottom cups with a Sharpie, and then punch them out from the frame. Turn them 90 degrees from your center line and then reinstall. What this does is to return the normal tolerances of the headset to the area of the headset that sees the most work during riding. See, a headset doesn't see universal stresses across the entire cup. The forward edge of the upper cup and the rear edge of the lower get more abuse during heavy riding conditions. After turning the cups, you will still have an indexed headset, it will still be damaged, but the forward normal position of the bars while riding will run the headset on a part of the cup that is undamaged. Only if you ride with your bars parallel to the frame, essentially in circles, will you feel the indexed portion of the cup. Even then it will just feel loose, as the headset will be properly adjusted to an undamaged portion of the cup and not the worn portion.
Ever wonder why you see some labeled headsets with cups facing in different directions than the norm? Say, a "Deore XT" headset with the writing facing to the sides and not the front/rear? That's not just because some people are weird and want to run the headset sideways, its because somebody has turned the cups.
Turn the cups, you'll be fine. While you're at it, make sure the headtube is faced properly. An unfaced headtube, or one with a bunch of paint on the ends will promote damage to a cheap headset faster than you can say 'Timberline!'
Good luck!
