Have there been any periods in earth's history where the rate of increase of carbon dioxide in the atmosphere equalled or exceeded the rate we're seeing today?  I'm curious because i've read that a rapid increase in co2 levels was a major factor in the permian extinction, but co2 levels rose even higher during the eocene without causing such a dramatic die-off.  Was the change in climate slower during the eocene, giving life more time to adapt?  What caused the high co2 levels during the eocene?

I believe the simple answer is "no."

One of the leading theories as to the cause of the Permo-Triassic extinction is the release of CO2 from volcanoes in Siberia known as the Siberian Traps. While these eruptions were massive, and sync very well with the timing of the extinction, they occurred over the course of about a million years, so nowhere near as fast current rates of CO2 release by anthropogenic sources.

In regards to the second part of your question, the climate change seen during the Paleo-Eocene Thermal Maximum (PETM) was indeed slower than modern climate change, but at the same time is one of the fastest instances of wamring in earth's history, making it a good study system for looking at envrionmental responses to rapid climate change. The cause of warming during the PETM is still debated, but we know from looking at stable isotope geochemistry that there was an influx of carbon into the atmosphere and ocean coinciding with the warming event. It's possible that this source of carbon was methane (CH4), not CO2, which could have been released from the deep ocean, but again this is all still being researched.

The take home message is that the amount of CO2 being released into the atmosphere since the industrial revolution is indeed much faster than anything earth has experienced before.

It is highly likely that the increased temperatures experienced during the PETM led to marked changes in the composition, distribution and phenology of numerous species of flora and fauna, without the mass extinctions (although there may have been local extinctions).

It also seems logical that the reasons that species could buffer such dramatic changes to life history timings, distribution etc. involve the rate of warming (slower than today) and the availability of 'other land'.

What we have today is a very rapid warming event (some species will be winners - generalist mobile, lots of others will be losers (specialists & sedentary)) and the double whammy of constrained land (for terrestrial species). For instance, if you are a 'cold adapted species', the response to rising temperatures are latitudinal (you head towards the poles) or altitudinal (you head up a mountain). Thinking of something like the mountain argus butterfly here in the UK, the warming projections are such that, very shortly, the species will have nowhere to go (our mountains are not high enough to be cold enough and once you reach the north of Scotland, there isn't any more land!).

Moreover, if you are a habitat specialist and you like warm situations (for instance, the silver-spotted skipper butterfly lives on south facing short turf grasslands), climate change might be beneficial. However, the only south facing short turf grassland we have here in England are predominantly in the south east and south coast, where most of the human population is. The remaining grasslands are only those too steep to plough or convert into housing and there is nowhere else for this species to move to, it is stuck in its specialist lifestyle. Happily, the silver spotted skipper has had a rise in population numbers over the last few years, due to targeted conservation management (scrub removal and appropriate grazing) but that is the equivalent of moving from intensive care to a general ward, the over-riding view is that the population for this (and most of our other butterfly species - which can be used as an indicator for the health of the overall environment) is rather bleak.

In short, we are looking at the local and large scale extinction of many species because of our impact on the climate and our demand for land, something far removed from the natural cycles of extinction and climatic change...

Ref: 'The State of the UK's butterflies'. R. Fox et al. British Wildlife vol. 23, #4, 229-239. 2012