Earth has had many mass extinctions, but about 250 million years ago something really, really bad happened. In an event known to paleontologists as "the Great Dying," life itself was nearly extinguished by massive releases of greenhouse gases. And by “massive releases” we mean “releases slower than what we’ve got going on today.”
Scientists at MIT recently established that the Great Dying happened even faster than they'd previously imagined, and that "the average rate at which carbon dioxide entered the atmosphere … was slightly below today’s rate of carbon dioxide release into the atmosphere due to fossil fuel emissions."
The good news is that the extinction happened faster than scientists thought, but not remotely what you’d call fast. The greenhouse-gas buildup required to accomplish the near-total extinction of the only known oasis of life in the entire universe took something like 20,000 years. So in order to reproduce the Great Dying, we'd have to keep up our current pace of burning fossil fuels for millennia.*
The current crop of Republicans will be all over that, but they’re headed for a Great Dying of their own, eventually. So: As long as Congress doesn't get access to some hitherto unknown life-extension technique, we're safe! Ish! Because in the meantime, "lesser" climate catastrophes are definitely on the way.
*Everyone who cares about the fate of life on earth should be a plaeoclimate geek. If you want to read more about the Great Dying, which literally poisoned the oceans and air with hydrogen sulfide through a downstream biological process, check out this excellent article on the subject by Peter Ward at Scientific American.