Others in the Pentagon and Obama administration feel strongly that nothing can be won on the ground until there are enough troops to do the job properly, if the mission is defined as remaking Afghanistan. They also argue (rightly, I believe) that if Afghanistan were again controlled by the Taliban, al Qaeda would have a safe haven of operation that we would rue, and a public relations and psychological victory that would help revive their cause.
The problem is that both sides are right. I am not an Afghanistan expert, but I have spent years in war zones where the government is viewed as corrupt and illegitimate (including the drug wars in Colombia, and the 1980s conflicts in El Salvador, Nicaragua and then, West Africa). Without state legitimacy there is no way one can create conditions on the ground for that government to take ownership of any sort of popularly supported programs.
The Karzai government, with its top-down corruption, disdain for action and embrace of massive fraud in an electoral process, appear to embody the worst of all the elements that drive people to take up guns in the first place.
Yet without the necessary resources, the war is lost and the most brutal option available -- hardliners who feel they have achieved the right to govern through military victory -- takes root. The Taliban in their earlier incarnation showed this. Either outcome leaves the U.S. vital interests damaged and the Afghanistan people thrown to the predatory wolves of either side.
The only real option (and it seems to be something Obama personally is asking about and thinking about) is to bypass the central government. A tribal/regional focus, as was initially done in Iraq, is the only way to stand up a fighting force against the Taliban while having a shot a helping to nurture local political and economic progress that brings some sense of legitimacy to the tribal leadership.
Once the security is established, one can move on the education fronts, economic fronts and all the other myriad issues that must be addressed. The draw back is that many of these tribal and sub-tribal groups are extremely conservative and do not share a vision of anything like a society in which women are equals, the education of girls is valued, and the rule of law (rather than the rule of the leader) is valued.
Such a path will also reinforce the tendencies in the nation toward separation and division, rather than create movement toward a unified country under a central government. But until that government is willing to give people something worth fighting for, their legitimacy won't be recognized anyway. The central government, to most in Afghanistan, is an alien and predatory force that has no positive relationship to their lives, and may have many negatives.
Clearly there are no good or easy answers. It seems to me that the local option is by the most viable in the short term. In the longer term, clearly issues of nationhood must be addressed. But Afghanistan won't get there with this government. It is too rotten, too corrupted and too illegitimate to bring anyone into the fold. Bypassing it to work with local leaders, with all the risks, is a better option.