I've had much better luck with forming taps. They work really well in those smaller sizes--especially if you're going to the trouble of making a lead-in chamfer.
If not that, then go up a size or two on the drill. An extra 0.003-0.005" ain't gonna' kill your threads but they'll tap much easier.
Also: are you absolutely sure that your predrill is deep enough? I had one where I thought I was going nuts, but the drill had pushed into the chuck on the first hole, causing them all to go shallow. I broke three taps before I figured out what happened.