My answer has a very narrow focus: Barack Obama went into office thinking that he could close Guantanamo. After he was briefed and tried to actually move the detainees out of there, he found out that that was not really an option.
However, he was convinced that it wasn't in the best interest of the United States to continue with the previous administration's policies and procedures to prevent attacks against U.S. assets.
Viewing the drone campaigns as a replacement for camp X-ray (as I said, very narrowly), the strikes are definitely a positive. The perception is that drone attacks are very targeted, with small, almost unavoidable, collateral damage. Drones are viewed as a credible threat for the bad guys, who are confined to bunkers. Anyone can be followed for weeks before action is taken, if any. Drones are almost mythical creatures.
The reality may be very different, but the image that no one is safe from the U.S. anywhere in the world because of spy drones is better than the idea that anyone could be abducted anywhere in the world and resurface at Gitmo. It seems "cleaner" and more surgical.
Regarding the other parts of the question, like long-term views: sending anything, even pint-sized drones into another country to spy on their citizens or kill them cannot be expected to be a good thing or even continue to be acceptable for anyone for an extended period of time.
Today, "desperate times call for desperate measures" can be an acceptable excuse, but in a few years when drones are not mythical anymore, the U.S. will need to be able to put them in context: as an additional tool in a tool belt where human intelligence, diplomacy, and even trade are equally considered and utilized. We can't just attack with drones every Taliban leader we don't like, we'll have to engage them and work with them eventually.
Also, when police forces and emergency services around the country start deploying their drones in our cities, an internal shift in perception should be expected. It is one thing to think that the president only has to push one button to kill one bad guy, and a very different one to feel Big Brother breathing down our neck in our daily lives.
Drones can be a great tool if they are properly used as Teddy Roosevelt's big stick while the U.S. talks very softly in the future.
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