It depends on how we define the moderate phase. In the early days of the National Assembly, the leaders of what would later become the Girondin/Brissotin and Montagnard/Jacobin factions shared a lot of the same ideas of radical social reform--even total moderates like Lafayette did--and what drew a number of politicians away from liberalism (including the Montagnards, when you consider their later support of sensorship, etc) was, aside from fear of invading armies which nothing could have helped, fear of the power of the mob.