Possible, yes in theory. Practical no. If the Northeast has excess water, you’d need to pipe it up over the Adirondacks and Appalachians to get it to the Midwest. Then up into or over the Rockies to get it to the west. I’m pretty sure the Northeast typically, but not always has more water than it needs and the Southwest almost always has less. It’s much harder to build the infrastructure and pipe water than to do the same for electricity. And the energy costs of pumping the water long distances would be very high I’d think.
Water’s a bit heavier than electricity, and consequently more expensive to transport. Also there are considerable technical challenges - e.g. how to minimise evaporation losses when moving water over long distances.
Can you transport water from one part of the country to another? Sure, but the feasibility and economic practicality of this depend on how big the country concerned is, and how mountainous is the terrain over which you wish to move it.
How much water could be transported with existing infrastructure? Say, with every tanker truck or train car that transports anything fit for human consumption. My WAG is that the country could transport enough water to keep people from dying of thirst in a pretty substantial region, but nowhere enough to support agriculture and livestock production.
One problem is that every time there is a drought out West and one of these water transfer plans begins to make sense, it starts raining cats and dogs out there. Soon all the reservoirs are at capacity and the excess water is dumped into the Pacific.
I think desalination plants along the coasts in CA and TX would work best. This way the states in the northeast would not have to be convinced to give up their water to those “crazies” out West who live in a desert, but want green lawns in front of their homes. All the rich oil states in the Middle East use desalination for their water needs, so the technology is there. The plants would just need the ability to be put in mothballs during wet years.