The only thing that he could do in order to prevent that outcome was to turn to the Party of Order.(Marx, 43-50) Although there had always been conflicts between the two parties, executive and legislative, they depended on each other in order to maintain the power. This is why both parties were willing to compromise, scared of the possibility they would no longer be able to enjoy the benefits of the revolution. If the second reason for which the parliamentary republic had to be maintained is connected with a temporary weakness in Bonaparte's status, the third one is connected with the fear of the bourgeoisie of losing its position. By the end of the second period of the French revolution, the universal suffrage was no longer available. In other words, it was very obvious for the masses now that the Party of Order had broken its promise and was functioning only as an instrument serving the best interest of a single class, that is the bourgeoisie. (Marx, 63)

In the meantime Bonaparte was continuing his own political plan and was black mailing the bourgeoisie in order to receive huge sums of money on a yearly basis. Although they were against him and did not fancy losing so much money from they own pockets, they could not declare an open conflict to the President because they needed him. All the small actions that they took against him created the feeling of unrest. The general atmosphere...

(Marx, 67) Under these circumstances the Party of Order understood that avoiding any decisive conflict with the executive was the only way to avoid revolutionary acts that would take away all of its power. Therefore the bourgeoisie allowed Bonaparte to have his way for two reasons. The first one was to avoid evoking revolutionary unrest. The second reason was to avoid appearing as an instigator of unrest in the eyes of their own social class.(Marx, 70) it is obvious to see that the only alternative they had was to maintain the parliamentary republic.
In conclusion, the parliamentary republic was the only possible government form fro the second period of the French revolution because it was the only instrument that could camouflage the dominance of the bourgeoisie and allow both bourgeois fractions (Legitimist, Orleanist) to maintain the power. While the interests of the executive and the legislative forces were often divergent throughout the period, as showed above, the survival of the Party of Order and of the parliamentary republic was the only solution through which the interests of the French bourgeoisie on the one hand, and of Bonaparte on the other could be maintained.

Bibliography:

Marx, Karl (ed. Dutt, C.P.) the Eighteenth Brumaire of Louis Bonaparte, with explanatory notes. Ney York International Publishers