There was opposition. There was a conspiracy involving Annius Vinicianus. He was supposedly moved to conspiracy after the death of Appius Junius Silanus. He had been suggested as a possible successor to Gaius and thus may have felt that he was viewed with some suspicion. He gained the support of the governor of Dalmatia, Furius Camillus Scribonianus, and Camillus attempted to move the troops into Italy. The soldiers refused and Camillus killed himself. Claudius responded by purging the aristocracy and Dio, 60.15, tells us that many men and women were killed, some being people of prominence. As always, there is doubt over how far the conspiracy went. Pliny, Epistles, 3.16, tells the story of Caecina Paetus, consul in 37, and his wife, Arria. Paetus was in Illyria with Camillus when the revolt fell apart. He was brought back to Rome and found guilty. Arria then encouraged him to suicide by killing herself and unconvincingly saying ‘nec dolet, Paete’ (Paetus, it doesn’t hurt).
What interests us is that she became something of a martyr for the anti-monarchic elements in the Roman aristocracy.
Asiaticus went to his death calmly, making arrangements for the funeral, a martyr. He had been involved in the conspiracy against Gaius, but is also seems that he adopted a philosophical stance. The accusation was wide-ranging, treason and adultery (Tacitus, Annales 11.4-6). point to an opposition which was more ideological, emerging from a philosophical engagement.