Italian campaign was to be a secondary theater, in the directoire original plan, to make a diversion and gets austria to divide its forces while the main thrust was coming in the germanies.
The quality of the troops and generals affected to it reflected this, as well as the numbers of troops available for operations ( when Bonapartes got commands, he could attack with 28000 men out of a theoretical effectif of 115000+ , IIRC, and the judgements he wrote about his immediate subordianates was .... less than enthousiatic).
Bonapartes intrigued to get the command and changed the plan without refering to Paris. He then endlessly clamored for reinforcement. To get these, he exagerated the importance of the theater.
Notheless, this was a secondary theater ( like Switzerland ) and the life of the republic was saved by the clash of armies in the low countries and germanies. Basically, while Austria lost some important territories here, a defeat wouldn't threaten Vienna, while a french defeat wouldn't spell the doom of the republic, as a defeat at say Fleurus may have.