The vascular system of the arborvitae cutting is still operational when it is removed from the parent plant. This means the cutting has the ability to draw some water up from the bottom of the stem. However, once the arborvitae cutting forms a callous over the wound, water absorption stops. Cuttings do not have roots that absorb all the water that is lost when the stem section is separated from the stock plant. The cuttings do not benefit from sitting in water for more than a day or two.
Two common words when working with cuttings is transpiration and desiccation. The act of water traveling through the plant and evaporating out from the leaves and stems is called transpiration. Under normal circumstances, the arborvitae roots absorb more water from the soil and replenish the lost water. If the arborvitae cannot absorb water, then desiccation -- drying out -- occurs. Strip the foliage from the bottom part of the stem cutting to slow the transpiration process while the cutting is in water. The less foliage there is, the less area the water has to escape from the cutting, and your cutting suffers less damage if it must remain in water for a few days.
Cool temperatures keep the transpiration to a minimum. For healthier cuttings, wrap them in a few damp paper towels and place the package in a plastic bag. Store the bag in the refrigerator for no more than seven days. Longer storage periods cause the stems to break down and possibly rot. You could set the jar of water and cuttings in the refrigerator for a day or two to minimize transpiration. For longer storage and a higher humidity level around the cuttings, use the moist paper towels and plastic bag.
The arborvitae cuttings can also rot when stored in water for more than a couple days. Even though the cuttings need water and oxygen, there are no roots to gather either one from a glass of water. The stem gets water-logged and the cutting dies. New arborvitae cuttings absorb water and oxygen from the humid environment surrounding the leaves and stems. This humid environment is created with a misting system or a clear plastic tent over the propagation chamber.