Fossil fuels are an integral part of the US energy portfolio, playing a prominent role for current and future domestic energy security. A sustainable, low-carbon future will require CO2 to be captured from major coal and natural gas power plants. However, fossil fuel electricity generation CO2 emissions are typically highly variable throughout each day with daily generation profiles varying greatly between plants. We demonstrate that understanding this variability is absolutely critical for setting a suitable carbon price as well as identifying if and how much CO2 a power plant will capture. For example, we show that a CO2 emissions price (or tax) of anywhere between $85/tCO2 and $135/tCO2 will be required to incentivize a gas power plant to manage all its capturable CO2; this range is solely due to differences in CO2 emissions profile. Further, we show that the setting a carbon price is very sensitive to system-wide costs including the CO2 value for enhanced oil recovery and, in particular, the costs for CO2 transport and storage. We also find that, even though coal-fired plants are more CO2-intensive and thus incur greater CO2 management costs, coal plants require a significantly lower carbon price ($15/tCO2 lower) in order to encourage CO2 capture. We conclude that integrating fossil fuel power, particularly natural gas, into a large-scale CO2 capture and storage system is a complex problem that will require detailed research and modeling.