The doomsday side is essentially advocating atavism - shutting down economic activity, and relying on grossly inefficient sources of power (how many environmentalists advocate the only sane option i.e, nuclear?) This will obviously have profoundly negative economic consequences. Especially in developing nations. No serious economist disputes this. In effect this argument is like saying that because car accidents cause a lot of deaths, the solution is to stop driving.
The "ignore it" side is basically claiming that this isn't a problem and we should just keep doin' what were doin'. So if this problem does end up biting us in the ass, we would be completely unprepared to deal with it.
But there are numerous solutions here. Nuclear power is probably the simplest. Helping developing nations industrialize is another - it's pretty well established that industrialization = wealth = less pollution. Then there are more radical solutions like installing CO2 scrubbers. The point is that technology always has costs associated with it. Nothing is free. What we should be concerned with is how to deal with the costs, rather than eliminate the life saving technology.