Answer: About one quarter
A US Geological Survey report found that from 2005-2014, fossil fuels extracted from federal lands accounted for anywhere from 22.0 to 25.9 per cent of total U.S. carbon dioxide emissions.
From Merrill, M.D., Sleeter, B.M., Freeman, P.A., Liu, J., Warwick, P.D., and Reed, B.C., 2018, Federal lands greenhouse gas emissions and sequestration in the United States—Estimates for 2005–14: U.S. Geological Survey Scientific Investigations Report 2018–5131, 31 p., https://doi.org/10.3133/sir20185131.