Recent suggestions that nuclear fusion might be induced in ordinary matter at room temperature motivated this study of the processes that influence the reaction rate in highly compressed matter. An approximate model that applies in the regime of strongly coupled plasma (Γ > 1) is developed and used to estimate the rates of the nuclear reactions: d(p, γ) He3, in hydrogen of natural isotopic composition which has implications for energy generation within the giant planets, and the dd reactions under conditions that might be or might have been obtained in the laboratory. The conclusions do not support the recent claims that this reaction occurs, at observable rates, in small electrolytic cells and suggest that compressively induced fusion of hydrogen is likely to be of importance only in large dense systems as may be encountered in astrophysics.