I now have all the source material needed directly from Guyton and Hall. Here is the answer:

In uncontrolled Diabetes Mellitus, blood glucose rises to very high levels. When plasma glucose exceeds approximately 250 mg/dL, the filtered load of glucose surpasses the tubular transport maximum and glucose can no longer be fully reabsorbed. This unreabsorbed glucose remains in the tubular fluid and acts as an osmotic diuretic - it increases the osmotic pressure of the tubular fluid, reduces water reabsorption, and causes large volumes of urine to be lost. This results in polyuria.

The resulting polyuria leads to significant dehydration and volume depletion of the extracellular fluid compartment. Simultaneously, the loss of water in excess raises extracellular fluid osmolarity and plasma sodium concentration. Even a rise of as little as 2 mEq/L above normal in plasma sodium is sufficient to cross the threshold for the osmoreceptor-thirst mechanism in the hypothalamus, activating the sensation of thirst.

This intense stimulation of the thirst center drives the patient to consume large amounts of water - a response called polydipsia - which is essentially a compensatory mechanism to restore plasma osmolarity and extracellular fluid volume toward normal. As Guyton and Hall state directly: "one of the hallmarks of uncontrolled diabetes mellitus is polyuria (frequent urination), which is balanced by a high level of fluid intake (polydipsia) secondary to dehydration, increased extracellular fluid osmolarity, and activation of the thirst mechanism."

In summary: Hyperglycemia -> osmotic diuresis -> polyuria -> dehydration + raised plasma osmolarity -> hypothalamic thirst center activation -> polydipsia.