I am not so sure that a majority of the current supremes hold with the "Living constitution" idea.
The idea of a "living constitution" has not been held by the Supremes to be a matter of constitutional law and it absolutely is not mentioned in the Constitution. Justice Ginsberg probably comes the closest of the current Justices to using this idea in her rulings. I am not at all sure about how Justice Sotomayor or Justice Kagan feel on the matter. So far they do not appear to support such a construction. Justices Thomas and Scalia have been vehemently opposed to the idea. The late Chief Justice Rinequest was opposed to it
Where Britain had a hook (which began as the divine right) from which to hang a government, the American colonies did not, thus the written constitution as a foundation from which to govern.