. . . where Shiites are the majority, and with whom he'd already fought a war.

Second guess: Israel -- not a real threat to Saddam, but a perceived one, on G.P.s.

But here's where it gets tricky -- a variation on Tom's theme from a year or so ago, when it began to become apparent that the WMDs weren't there:

Tom speculated that perhaps the scientists running the weapons program were making false reports to Saddam without actually making any weapons. Dangerous, but not without precedent (cf. the USSR). The result being: Saddam thought he had 'em, when he didn't.

My take on this is a little different: the "difficult balance" was between maintaining the posture of having the weapons, while not actually having them. As long as he could keep the the UN inspectors out, he could keep the other countries in the region on their guard, and look like he had big ... socks.* But once all the bluffing failed and the inspectors got in, they wouldn't find him out of compliance with the resolutions concerning weapons.

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* see Monstrous Regiment, by Terry Pratchett, which I just read.