Let's consider what would happen if the price per ton of CO2 emissions shot to $100 tomorrow. This is much higher than we're likely to see in the near future, of course, but it's useful to understand what might happen a couple decades down the road. It translates into an increase in the price of electricity from coal of about 10.5 cents, enough to increase the whole cost of coal power to over 15 cents. At this point, many alternative sources of electricity become extremely competitive with coal, and indeed probably cheaper: solar thermal, nuclear, wind, combined-cycle gas, etc. The corresponding rise in the price of gasoline, on the other hand, is slightly less than a dollar. This is hardly insignificant, but it's smaller than the swings we've seen over the past few years, and not nearly enough to threaten the basic viability of car transportation.
To grasp the difference in magnitude here, I think it's best to look at a chart:
At current prices, coal power skyrockets 217% in cost where gas inches up only 38%. Gasoline (and thus car transportation) is one of the least responsive prices to a carbon charge, while coal power is one of the most. This is a good illustration of why explicit carbon pricing is so important—without it, we're liable to miss vast differences in the cost-effectiveness of different strategies to reduce emissions. Coal is the low-hanging fruit; motor vehicles are not.
*To arrive at these numbers, I used data on the carbon intensity of coal available here and on the carbon intensity of gasoline available here. I took the price of coal generation from this MIT report on the future of coal, averaging the prices for the four standard types of coal generation on page 19 and adjusting slightly for inflation since the report was published. Gas prices are taken from EIA data here.
Edit: As Prent points out in comments, I forgot to define my units! The coal price is in cents per kilowatt hour.