This is one of the big questions even among professional historians! There are a lot of different factors that pushed participants in the Revolution to turn more "radical," and it's important to remember that this also includes events that were going on outside of France, too (e.g. the Haitian Revolution).

You seem to have one important thing down: before 1791, very few men in the legislature supported a republic. Most were in favor of a constitutional monarchy. However, there are a couple of key events to keep in mind that "radicalized" their opinions on the shape of the government:

1. Louis XVI's attempt to flee France - until June 1791, it seemed as though the king had tacitly lent his support to many of the National Assembly's actions, albeit begrudgingly. Having the king's support was an important justification for many of the early reforms. But when Louis attempted to escape with his family to rejoin émigrés who had sided with Austria, many Frenchmen viewed him at least with suspicion, or at worst as a traitor. A lot more men suddenly began thinking about France without a monarchy. The king's attempted flight was a catalyst for further radicalization in 1791 and 1792, and a few historians have argued that this was pretty much the beginning of the end for the monarchy (Louis XVI was executed in January 1793). For more on the king's flight, see Timothy Tackett's When The King Took Flight.

2. Increasing domestic unrest from summer 1789 on - A string of bad harvests and the Great Fear of 1789 were really only the beginning; an increasingly dire situation of domestic unrest unfolded in tandem with the king's attempted flight. Food riots in early 1792 demanded drastic solutions, and a royalist revolt in the Vendée a few months later touched off a bloody civil war that would last for the next four years. That's not even mentioning the slew of new laws and regulations that the state had to somehow find a way to enforce: loyalty oaths for the clergy and the seizure of church property, the abolition of feudal privileges, and simply the day-to-day running of the country (e.g. the managing of a new paper currency). These were problems that demanded drastic solutions, pushing a great many members of the Convention to support radical policies. This was just a small piece of other domestic crises occurring at the time (Jean-Paul Marat was assassinated in July 1793, for example, and became a kind of Jacobin martyr). This, of course, culminated in the Terror, but there were many steps along the way that contributed to it.

3. War with pretty much the rest of Europe - this is probably one of the most important factors to consider. Almost since the beginning of the Revolution, the threat of war with Austria and/or Prussia loomed over France. Those fears were justified when Louis XVI attempted to flee, and his subsequent execution exacerbated an already volatile diplomatic situation. If you want to know more about the war itself, check out John Lynn's The Bayonets of the Republic: Motivation and Tactics in the Army of Revolutionary France, 1791-94. But the war also mattered off the battlefield. The war against the First Coalition demanded a huge campaign to marshall soldiers and resources amidst all the other turmoil occurring at the time. Ken Alder's Engineering the Revolution: Arms and Enlightenment in France, 1763-1815 has an entire chapter about the difficulty the state had setting up munitions factories to supply the Revolutionary armies. That's one small factor that's really interesting to think about: both the introduction of conscription and the state's direction of the war effort required a massive mobilization of resources, all amidst the problems mentioned above. This is one of the reasons that the Constitution was suspended in October 1793 and the government declared "revolutionary until the peace" - desperate times called for desperate measures.

A fantastic general overview of these years is David Andress' The Terror: The Merciless War for Freedom in Revolutionary France. The book is very readable (it's written more for a popular audience) and gets at the reasons behind the radicalization of the Revolution.