I would agree the Romans likely did not take a slave revolt seriously as a military threat–they certainly took them seriously as a general threat, but probably did not expect them to defeat trained soldiers. That being said, I believe the initial forces that they defeated were more akin to irregulars pressed into quick service, and not Rome’s best troops. I know the praetor that was defeated by him at the base of Vesuvius is very frequently portrayed in fiction as a major villain of the story and generally shown to be inept. He likely was inept, but we also know almost nothing about him save his name and that he supposedly took a force of around 3,000 men. I think at the point that happened there was a perception that Spartacus men were more of a civil uprising or a bad case of banditry, it wasn’t recognized as a military force.
Taking a walled city was difficult in that era with a force still mostly of irregulars, armed with what seized weapons they could find and what bronze and iron they could trade with merchants.
There are a couple histories that record Spartacus defeating Roman consular armies, albeit the narrative is different depending on which historian you read–both histories agree that a force under Crixus was defeated by the army of Consul Lucius Gellus in 72 BC, near Mount Garganus. Appian’s history says that after Crixus’ defeat, Spartacus began to move his main force north, where the other consular army under Lentulus attempted to bar his path–Appian records that Spartacus defeated this army, and then turned to likewise defeat the army of Gellus who had been coordinating with Lentulus in an attempt to catch the slave army between them. Appian then records that the two consuls regroup and engage the slave army near Picenum, and were defeated yet again. Appian’s history marks this as being about as far north as Spartacus gets, and records that he turns around and heads back to Southern Italy.
Plutarch’s history differs in that it does not record Spartacus ever engaging the army of Consul Gellus directly, instead just noting he defeated the consular army of Lentulus on his way north, and that in fact Spartacus took his army as far north as modern Modena which is getting fairly close to escaping Italy. Plutarch then records a clash between Spartacus and the Governor of Cisalpine Gaul, Gaius Longinus, whom Spartacus also defeated. Plutarch’s history than has quite a gap and makes no real explanation of why this is the furthest north Spartacus goes, and does not update on the war until the next year.
It is interesting if Spartacus made it as far north as Modena why he didn’t really try a break out of Italy, especially if as Plutarch records he defeated the armies of Cisalpine Gaul already.
We do know from Hannibal some 130 years before sieging Rome was likely no small affair, Hannibal worked diligently to try to build enough support from Italian cities to get positioned to take Rome, Appian’s history mentions Spartacus had attempted to get the allegiance of some of the cities in his area of operations but was unsuccessful–we do read in both histories that shepherds and peasants did join the slave army for reasons unknown, possibly just general unhappiness with Roman governance.
It’s also interesting the way Spartacus lead the army, if we compare it to slave uprisings in the New World, a big limiter of those uprisings was usually that the leaders were very limited in how much they knew about the geography of the area around where they were enslaved and were massively uninformed on military tactics and operations. This is why a typical New World slave revolt 1900 years later or so was never much more than a really nasty riot in most cases, even the one that lead to the independence of Haiti was not well organized but won on sheer force of bodies. If the histories concerning the Spartacus slave uprising are true he all but had to have had some experience in an organized military context, possibly as an auxiliary with Roman legions, and he had to have had good knowledge of the Italian peninsula and general logistics and strategy, a somewhat odd amount of knowledge for a slave to hold. Several Roman writers mention he had some sort of background in the legions, but there’s no real biographical information on him outside the context of the slave war.