Very very very hard, since, after the quasi-protectorate agreement signed by Lesseps and Mazzini had been reneged by N. III, Oudinot had about 30.000 men in his expeditionary force, a thoroughly overwhelming force. Let's also not forget the presence of Neapolitan (as incompetent as they proved to be), Spanish and especially Austrian contingents occupying other parts of the Papal States. The only chance is Napoleon accepting the treaty, leading to a survival of the Republic in Lazio, Umbria and possibly Marche, losing at least the Legazioni of Bologna and Romagna to Austria. But this is in itself an almost impossible outcome, given that Napoleon's Catholic powerbase would never accept France being the steward of a Republic that caused the Pope to flee from Rome to Gaeta.