One idea is that "the constitutional civil liberties doctrines developed by judges throughout the 20th Century" don't fit the post-9/11 conditions.
Another would be to decide that the administrative state — "a bloated bureaucracy with serious accountability problems" — violates separation of powers.
And maybe the one-person-one-vote approach to legislative apportionment would no longer be seen as an Equal Protection requirement.
And maybe the privacy rights decisions could be seen as "written against a background of hysteria about a 'population explosion'" that no longer exists.
[T]he United States — like many other countries — faces not a population explosion but a baby bust, with birth rates too low to sustain population, or to produce enough workers to fund retirement programs for the elderly. These decisions were also followed by a breakdown in family structures that continues to get worse. I can imagine a “living Constitution” conservative concluding that, whatever the logic of these decisions is, experience has shown them to be too flawed to survive.The "living constitutionalist" liberals are mostly confident that the Constitution only grows in their direction and thus that conservatives can't get anywhere with their theory.
(That's similar to the way "progressives" feel complacently good about progress — visualizing it out there in the future as a place we want to go. How do they know we'll like it when we get there? Why don't they worry about other progressives progressing us into a place that doesn't look like what they dreamed?)