It is often assumed that coal miners view the possibility of a carbon tax or cap-and-trade program as a threat to their livelihoods. I'm sure that's true: that they view these as threats. What's not so clear is whether or not they really are threats.
While coal production in the US increased 32 percent between 1980 and 1999, coal-mining employment declined 66 percent, from 242,000 to 83,000 workers. Further, jobs in the coal industry are expected to fall by 36,000 workers between 1995 and 2020, even without any greenhouse gas–reducing policies, such as carbon caps or taxes, in place. [Source: Kammen, Kapadia, and Fripp, "Putting Renewables to Work: How Many Jobs Can the Clean Energy Industry Generate?" p. 14 (pdf)]
Update: the Bureau of Labor Statistics has numbers for 2008. Total employment in coal mining, from CEOs to hoist and winch operators: 78,340, down 5 percent from 1999.
In other words, the threat to coal miners' livelihoods exists even if nothing at all is done to combat global warming. On the other hand, if one of these policies is adopted, it will surely include some kind of "transitional assistance," such as job training programs, subsidized loans for new businesses starting up or moving into coal producing areas, and so on. That assistance is less likely if climate legislation is blocked. So coal miners have a bleak employment future ahead of them no matter what. The closest thing to a ray of sunshine they can hope for is strong climate legislation that opens the doors to new industries and job opportunities to replace the coal jobs that are already doomed.