"History" and "stuff in the Bible" are very difficult to try and keep together, but there are a few facts we can build off of.

Was it the punishment that the Romans inflicted commonly on religious zealots and the like? Was crucifixion a threat to them at this point for upsetting the order that Romans held so dear?

Entirely so. Crucifixion was the worst form of execution available at the time. The bit about bearing the cross comes about because the condemned was forced to carry the cross he would be crucified on to the execution site. It was most commonly used in Rome as a means of executing slaves who turned against their masters, but also for enemies of the state. While it's most commonly held that Jesus was executed for blasphemy, which in itself was a capital offense at the time, the biblical sources seem to more strongly point to his offense being insurrection, noting from his being forced to carry a sign labeling him "Jesus, king of the Jews". Insurrection was the most common cause for death by crucifixion outside the slave class.

As for the line in question, Jesus was warning his followers that they were facing the worst possible death they could imagine if they followed his instructions, but that they were unworthy if they failed to do so.