From a recent CBO report [pdf; pg. 21]:
Despite the wide range of projected impacts of climate change over the course of the 21st century, published estimates of the economic costs of direct impacts in the United States tend to be modest. Most of the economy involves activities that are not likely to be directly affected by changes in climate. Moreover, researchers generally expect the U.S. economy to grow dramatically over the coming century, mainly in sectors (such as information technology and medical care) that are relatively insulated from climate effects. Damages are therefore likely to be a smaller share of the future economy than they would be if they occurred today. As a consequence, a relatively pessimistic estimate for the loss in projected real (inflation-adjusted) U.S. gross domestic product is about 3 percent for warming of about 7 degrees Fahrenheit by 2100.
However, such estimates tend to mask larger losses in subsectors of the economy. Some sectors in certain regions are likely to bear sizable costs requiring significant adjustments and adaptations, and a few sectors in a few regions may be eliminated altogether.
The last paragraph is applicable to the rest of the world as well. Countries with greater reliance on agriculture or fishing may face a much greater economic burden than countries that produce manufactures or services. The costs of climate change will not be borne proportionately.
While 3% of GDP is not insignificant, it is not disastrous either, and the costs of slowing climate change could be much, much higher. According to an oft-cited report by British economist Nicholas Stern, it will cost 2% of global GDP per year, every year, until 2020. At a glance, it seems like an easy choice: 3% is greater than 2%, so it would be cheaper to spend the money now to save it later (if you don't bother discounting). But in fact, the 2% figure must be compounded to find the true cost.
Suppose the U.S. will not have any economic growth between 2010 and 2020, so GDP remains constant at $14tn/year. Under that scenario, if we sacrifice 2% of GDP per year to combat climate change, then our economic growth rate is -2%/year, and our GDP would be $2.5tn lower in 2020 than it was in 2010, or roughly 18% lower. 18% over ten years is a much greater expense than 3% over 90 years. (This assumes that there would be no economic growth until 2100 as well, which is unreasonable, but it doesn't change the substantive conclusion; it just shifts the numbers a bit.)
But that's not all; GDP would also be lower in each of the other years from 2011-2019, and these totals must be summed to get the full cost. If my math is correct, the total cost would be about 90% of 2010 GDP, or roughly $12.6tn.
But that still doesn't cover it. Because we have sacrificed 2% growth per year from 2010-2020, our GDP will also be lower in every future year until the end of time at an increasing rate even if we stop all spending on climate change prevention measures in 2020 (since foregone economic growth cannot be recovered). In other words, the cost of stopping climate change is infinitely high if your time horizon is long enough, but is extraordinarily large even in the short run.
Now this back-of-envelope analysis depends on these estimations being correct, and they very well might not be. Different inputs will yield different outputs. The Stern Review, for example, predicted much higher (global) economic costs for inaction than the CBO report and advocated massive, immediate action to prevent climate change. It may also be possible to slow or stop climate change at a lesser expense, although I have not seen a credible estimate lower than the one provided by Stern. I think it's quite possible that a different analysis could find that it is economically beneficial to spend heavily in the short run to prevent large economic damages in the long run. But conversations about how much we should be willing to sacrifice to slow or stop the warming of the earth must get its terms correct, and this starts with a proper understanding of the nature of compounding growth rates. And discount rates, but that's a discussion for another day.
Postscript: I have intentionally left normative arguments off the page. For some, preserving nature may be worth it at any cost; for others, nothing matters but dollars and cents. Personally, I am somewhere in between. I suspect most people are in a similar boat. These judgments must be made individually, but properly conceptualizing the positive implications of different feasible policies is necessary for forming a consistent normative judgment.