Adaptation AND Mitigation
I don't think you'll find an environmentalist or climate scientist who doesn't think we should be adapting to either already-existing hazards or to their climate-change-caused cousins. The world has already experienced a small degree of human-induced climate change, and the latest science makes clear that we're locked in to a substantial additional amount solely on the basis of the gases we've already emitted. At most, you'll find some who are leery of talking too much about adaptation because they think it will distract from the importance of mitigation, leading people to take Monka's position that adaptation alone is sufficient. I think such people are wrong about the distracting effects of adaptation talk, but right about the insufficiency of an adaptation-only approach.
The first problem with adaptation-only is that adaptedness is not a yes/no proposition. A given society is not "adapted to drought," for example. It's adapted to droughts within a certain range of severity, length, and frequency. So the level of adaptation necessary to deal with today's droughts may not be adequate to deal with the more severe, common, and long droughts that would occur as a result of climate change. Thus mitigation would limit the degree of environmental stress to which we're trying to adapt, making adaptation easier and less costly.
Exacerbating this is the fact that climate change is also not a yes/no proposition. We frequently hear climate scientists predicting things like "a 2-4 degree rise in temperature by 2100." This can create the misleading impression that the climate will go up a few degrees them stop at the higher level. But in fact it will keep going up as long as we're producing additional greenhouse gas emissions* -- perhaps 8 degrees above the present temperature by 2200, 16 degrees by 2400, etc. Given the point made in the previous paragraph, at some point the change will be too much and it will overwhelm our adaptation measures.
Another concern is the impact of climate change on non-humans -- wild animals and ecosystems. It's far easier to adapt human societies to climate change than it is to make similar adaptations for the rest of nature. If a climate-induced drought hits the northeast U.S. and dries up the Hudson, the people of New York City (and their pets and their gardens) can drink from a desalinization plant -- but what are the deer in the Adirondacks going to do? The natural adaptive capacity of animals and ecosystems is already stressed by human impacts. Their ranges and population sizes (and hence genetic diversity) are limited by human encroachment, and the fragmentation of the landscape makes it extremely difficult to adapt by migrating northward. Meanwhile the change is occurring too fast for the evolution of most species to keep up.
The final issue I'll raise is the questionability of proposing a strict tradeoff between mitigation actions and adaptation -- the implied model that there's some pool of money that we're willing to allocate to climate change measures, which must then be divided up among mitigation and adaptation policies. On the one hand, there are policies that do both -- for example, shifting from industrial monocultures to local organic farming is both adaptive (because monocultures are notoriously fragile) and mitigative (because less fossil fuels are used). But even with policies that are clearly located on one side or the other, the tradeoffs are not as stark as they may appear. There's good reason to believe that many adaptation and mitigation policies will be net economic boons, rather than costs. And even when they're costs, the costs may be borne by different actors, making them not fungible between mitigation and adaptation policies -- foregoing emission caps on coal plants does not free up the electric company's money to be spent by the water company in upgrading its system to deal with drought.
The proper response to climate change, then, is to adapt and mitigate.
*There's a possibility that other factors besides deliberate action to curb climate change may limit our emissions. The main candidate here is Peak Oil -- it's reasonable to imagine that by 2100 (or before), we'll be out of feasibly recoverable oil supplies. However, we have hundreds of years' worth of coal in the ground. Aside from climate mitigation, there's little political will to limit exploitation of coal to replace oil (either to generate electricity or for coal-to-liquid schemes). Considering that neither Clinton nor Obama is even willing to take a clear stand against mountaintop removal mining -- the most egregious and deadly practice of the coal industry -- I would predict that the government will end up subsidizing coal expansion in the event of a clear recognition that we've hit peak oil.