Since implementation of the northern no-fly zone after the first Gulf War, the Kurds have been working steadily towards autonomy. It's a little less confrontational than an outright declaration of independence, especially since Turkey and Iran would be just as upset as Iraq about the Kurds forming their own country.
The Kurds have been seeking their own country ever since European countries started withdrawing as colonial powers. Unfortunately for the Kurds, the region they habitat spans at least three different countries, leaving them a big minority in all three. Small scale uprisings that threatened to turn into a full-fledged revolution resulted in Hussein attacking the Kurds with chemical weapons. Up to 180,000 Kurds were killed by the attacks.
The Kurds did think they would receive support from the US after the first Gulf War, but I don't think they realized that the extent of the support would be enforcement of the northern no-fly zone. While they mounted a small scale 'insurgency', they still couldn't go to full-scale revolution when Hussein could still send in ground troops. Still, even if the support was less than what the Kurds expected, it did allow the Kurds to push their autonomy further and further without throwing Turkey and Iran into fits.
The Kurds at least seem a little more 'deserving' of help than the rest of the Iraq, considering they've been working towards independence for a long time, but now they're a problem. One thing you can count on is that the Kurds will eventually have their own independent country. It would be better for the US if that took awhile. A quick break-up of Iraq wouldn't help our hopes of reducing troop levels and, hopefully, getting out of Iraq completely within a reasonable amount of time.