Logic programming with the stable model semantics has been proposed as a constraint programming paradigm for solving constraint satisfaction and other combinatorial problems. In such a language one writes function-free logic programs with negation. Such a program is instantiated to a ground program and its stable models are computed. In this paper, we identify a class of logic programs for which the current techniques in solving SAT problems can be adopted for the computation of stable models efficiently. These logic programs are called 2-literal programs where each rule or constraint consists of at most 2 literals. Many logic programming encodings of graph-theoretic, combinatorial problems given in the literature fall into the class of 2-literal programs. We show that a 2-literal program can be translated to a SAT instance in polynomial time without using extra variables. We report and compare experimental results on solving a number of benchmarks by a stable model generator and by a SAT solver.