Cap and trade systems were devised by (mainstream and conservative) economists who think it would be better to use economic forces and markets to gradually bring about changes, rather than use command and control government regulations.

In a coal cap and trade system, existing users (power plants and industry) would be given coal use credits based on how much they are using now. Those credits could be sold or transferred. If someone absolutely had to use coal for a new power use, they would have to go out and obtain credits from someone else that had them. If a coal plant somewhere converted to something that was carbon free (nuclear, wind, solar, geothermal, etc), then they would be in a position to sell the credits that they had been using for the coal plant. Selling them would help fund the conversion to less polluting sources of energy.

These type of last minute alarmist warnings are rather boring - especially when they are based on distortions. Obama would cap coal use at current levels, not close down the entire industry.