The Babylonian wise men stand completely helpless before the king's impossible demand, openly confessing the limits of human intellect. They declare that the mystery placed before them crosses the boundaries of human ability and belongs entirely to the spiritual realm. The matter the king asks is extremely heavy, difficult to grasp, and entirely beyond human solution. Alternatively, the request is of such a high and honorable nature that it is only fitting to bring it before higher powers, rather than flesh and blood [אבן עזרא, ביאור שטיינזלץ].
At the same time, their response carries a layer of flattery. They suggest that since the king's own wisdom is so great, any riddle he cannot solve must be uniquely difficult. They reason that no ordinary person could possibly match his intellect to solve what he could not, leading them to believe he is merely testing them [אלשיך].
When the wise men claim that only divine beings can solve such a mystery, the primary approach among commentators is that they are referring to the upper angels, who exist without physical bodies and do not live among mortals. These angels are pure spiritual forms of truth, and human souls are actually derived from them. Because human souls are confined within a physical body, they are limited in their ability to understand hidden matters. They can only catch slight glimpses of these secrets, mostly through dreams at night, when the soul experiences a temporary release from the physical demands and troubles of the body [אבן עזרא].
A deeper layer of meaning is found in their admission that there is no one else capable of providing the answer. Their words secretly hint at the High Priest. The wise men essentially confessed to the king that the only individual who could possibly reveal the dream's solution would be the High Priest wearing the Urim and Thummim, but he was no longer available. This honest admission sparked the king's fury. He challenged them, demanding to know why they had advised him to destroy the Temple if it held such immense power, and he immediately ordered their execution [רש״י, מנחת שי].