García Méndez was a member of the Puerto Rican Alliance and in the elections of 1928, was elected to the Puerto Rico House of Representatives by the electoral district 18. By 1932, he was a member of the Republican Union and was named to the first Territorial Executive Committee of the Republican Union. In the elections of that year he was re-elected to the House of Representatives by the same district. In the following elections he was re-elected to the House. This time as an at-large candidate (statewide).