Concerning how the republic and early empire Romans looked upon Alexander and his military might, I came across two interesting sources.

In his History of Rome, 9.17 - 9.19, Livy argued that if Alexander did invade Italy he would be utterly destroyed. And in the life of Pyrrhus, Plutarch recorded the Romans of that time also made the same assertion.

Those two were both armchair historians, not sure if Arrian or Polybius ever made similar predications.