I don't see why either side would object to this. Democrats keep saying that their political nirvana is a country with higher federal taxes, more federal regulations and more federal government spending. Well, let them have it! If they had a decisive political majority in a country that's half of America, they could have all of that -- and more. How could they possibly complain?
Same goes for the Republicans. They want fewer federal taxes, less federal spending and less federal regulation. Divide the country into two, and they could have it all. I don't hear a single Republican who would complain.
How would this work, practically? One party could have no more than 25 of the current states, where a minimum of 23 would be geographically consecutive, assuming the same entity also had Hawaii and Alaska. It would probably have to leave room for each half having at least one state on each of the two oceans. Practically speaking, that would, in turn, mean that California and Washington state could not be part of the same country -- the question is which would be which. Other than that, almost every combination would be possible.
Clearly, this would have to entail moving, for close to half of the population. The real solution here would be one of natural selection, where people would do it over some period of time. Americans moved before, such as in the 1800s when they headed West, and they still move today where some states show large net immigration numbers and other states have been de-populating for at least a decade or two. With more change and distinction, chances are that this new migration would be faster and more pronounced.