Well, the Carthaginian citizens were often willing to fight and die
It is said that when the Roman senate convened following Cannae, two thirds of the senatorial body was missing. They had sacrificed their lives for the Republic. Meanwhile, in Carthage, the senators were sitting on their plump arses and, led by anti-war politicians such as Hanno, trying to call Hannibal back home. This is a generalization but you see what I mean.

the Italic allies of Rome (not the Romans themselves) were often willing to change sides if the Carthies looked like they were going to win (as happened on a large scale during the Second Punic War
Indeed. This is probably what Hannibal was intending to play on when he invaded Italy--the support of disgruntled Italian allies. According to Livy I believe, he told Italian soldiers captured at the Battle of Lake Trasimene, "I have come not to make war on the Italians, but to aid the Italians against Rome."

More problematic to Carthage was internal division; the Romans never questioned whether they had to expand into Sicily and later along the Mediterranean coastline into Iberia.
I'd have to disagree on this point. The consuls of Rome were often members of the Fabii family, or their allies or subordinates. They were conservative, moderate, and never set foot outside of the Italian peninsula. However, for reasons unknown, the contemporary generation of Fabii were rather apolitical. As a result, another major family, the Claudii, held influence. Luckily for the Messanians (who were appealing to Rome for help prior to the First Punic War), the Claudii were expansionists who had a great interest in Sicily and had been pushing for Rome to build a fleet for 35 years now. For this reason, the Messanians appealed to the Claudian administration.

My point is that there was political division.