It's tough propping up a government when said government seems to want to fight you every step of the way.
Hamid Karzai has gone on a recent bender of accusations against, in particular, the United States, but also the UN and NATO in general. The particular meat of the accusations is that Western powers have "meddled" unjustly in Afghan elections, undermining the legitimacy of said elections and giving the Taliban a political talking point (specifically, the most recent rants mention the throwing out of 1/3 of the votes for Karzai in the first round of presidential elections).
The accusation is probably rather preposterous, but I might be wrong. Either way, the lower house of the Afghan parliament unanimously (that being everyone) voted against Karzai's decree that the UN can no longer hold 3/5 majority of the electoral fraud commission--instead, Karzai would himself appoint the entire body. Unfortunately, the upper house (1/3 of which are hand-picked by Karzai) decided that, procedurally, they could not vote on the matter within a year of the elections. Unfortunately, this means the decree will stand. for the indefinite future.
This isn't the first worrisome think Karzai has said about his relationship with the West. Recently, a visit by Ahmedinejad prompted Karzai to call him a "brother" and otherwise generally cozy up to Tehran. Karzai occasionally has fits about throwing out the Western occupiers, despite his dependence on them to keep his government afloat.
Karzai is, no doubt, a very frustrating character for the West. Somehow, the US has managed to build a relatively rosy relationship with a country that it is illegally invading and drone-missile-attacking to squash a Taliban force that said country has some interest in maintaining (this, of course, being Pakistan), but has not managed to keep on good terms with the tinpot dictator it's trying to support. I'm not quite sure whether Clinton has muttered the words, "Well, if you really don't want us..." but Karzai might just understand that the US (and in particular, the administration) has so much to lose that unilateral withdrawal is just not an option--and if that's the case, Karzai has a great bargaining position, despite his relatively flaky power.
It's not actually all that uncommon for a propping state to have trouble keeping its client state's leadership in line. al-Maliki has been a mostly excellent partner to work with, but this is the exception. The US and UK often fight bitterly with Israel; the US leadership groaned famously over the Saigon government in Vietnam, the KMT/GMD in the Chinese Civil War, etc.
But the question that comes to mind is this: why should Karzai be such a darn pain the butt? What incentive does he have to make the lives of the US leadership as difficult as he does? Wouldn't his life be easier if he wasn't publicly ripping into his supporters? Can't we all just get along?
Well, as you probably know, Karzai's in a pretty tricky position. As much as he loathes the Taliban at a very personal level, Afghanistan is obviously a very long way from being a Taliban vs. anti-Taliban kind of show. All those pesky warlords, tribes, ethnic groups, and what have you make Iraq look like Disneyland in terms of being able to reach a unified consensus and build a unified state.
At the end of the day, Karzai's got to make a lot of rather unsavory people happy enough that they won't directly challenge his claim to power. He's also got to build legitimacy with the general population, so they'll throw support behind him directly (meaning that the other power players in Afghanistan also have to side with Karzai to keep their own popularity and legitimacy). Karzai's in a rather precarious position.
And so, of course he's going to be rather cross when a little election fraud here and there (which he may not have even ordered personally) gets dragged out of the gutter and displayed for all to see--it's going to cast a whole lot of doubt on his personal legitimacy that he probably believes would not be cast if everything looked peachy. At the same time, of course he's going to get friendly with the Iranians--Iran and Afghanistan share a border, and Afghanistan's got a non-trivial Farsi-speaking minority that Karzai needs in his opus-coalition in order to keep power.
And it makes sense that Karzai would call Clinton right after to apologise--there may be a frustrated understanding that Karzai has to look tough against the US in order to try to build legitimacy among (the winnable) tougher nationalists or Islamists, and to show that he isn't implicitly condoning the prevailing impression of election fraud (without selling out the ground-level loyalists that worked so hard to stuff ballots and intimidate voters--such a rebuke would seem like an implicit betrayal).
So the guy's in a pretty tough position. Combine said position with a truly maniacal obsession with defeating the Taliban, a slightly-bigger-than-healthy paranoia, and a penchant for micromanaging that verges on power-obsession, and you've got the Karzai we know and groan today.
But what can be done about it? Well, this is the tough part. Ultimately, the leadership positions of Afghanistan need to be shored up without turning them into tyrants in order to do so.
The big win is probably going to come in developing the Afghan army. When regular folks in Afghanistan see the friendly neighborhood soldier keeping them safe and helping them out, there will be a lot more state buy-in. This can, in theory, be done in time (the New Iraqi Army was mostly built from scratch after the US de-Ba'athification... but it was tough). Furthermore, said army will make the local warlords a decreasingly viable alternative and decreasingly important force in the new Afghanistan.
Second, NATO has to show that the Taliban is a losing alternative. To this end, first, NATO needs big, flashy, high-profile victories in places like Marjah (which haven't yet been delivered, because they are militarily difficult). Second, NATO needs to win the PR war by showing that the Taliban are actually baby-killing extremist nutbags, and won't make life better for the average Afghani. Somehow, this is easier said than done.
Finally, the local police & administration need to be developed. This will be toughest of all. As you've probably heard a bunch, Afghanistan is not used to having any sort of serious central authority. Current administration is underpaid and corrupt, either selling out the central government for cash (usually from the Taliban) or thugging on locals to help prop up their warlord, or even the state. (Step one here is clearly to use our vast sums of wealth to start paying police officers more, and hire cross-functional accountability officers).
But it's going to be tough. Karzai's going to continue to be a problem for the West, and the West is going to have to live with it and work with it, or lose Afghanistan. But the friction between Washington and Kabul shows that we've got a very, very long way to go.