At the Constitution's ratification, original meaning and consent coexisted. But with the advent of a new generation, the Founder's consent faded and died. To justify constitutional governance of the living requires the force of their living consent.
How can we win the consent of the governed? Only imperfectly, to be sure. The Constitution is not a contract. But we can best justify it by reading it as if it were a contract. More specifically, we should regard it as a standard form adhesion contract offered by the federal government to prospective subjects. The feds don't offer a terrible deal, as such things go. Those who attended the ratification debates accepted the offered Constitution, after all. But their choices do not very well bind us--not, at least, if justification relies on consent.
A court interpreting a standard form agreement would adopt the same approach. Suppose, for example, that Hertz first rolled out its standard form contract in 1953. Among other things, the contract said Hertz would provide a "safe" vehicle. The new contract was proposed to many various consumers and won the assent of many, thus bringing it into effect. But Hertz cannot cite that ratifying consent as binding on me; it must win my assent anew. And any court worth its salt will, if asked to interpret the contract between Hertz and me, inquire as to the public meaning of the words as of when I signed. Hertz cannot, in other words, cite the original meaning of the contract to try to fob off on me a car that has no seatbelts. That might have been "safe" in 1953, but it is not within the reasonable public meaning of the word, now.
By extension, we should reject Scalia's claim that the Constitution today permits public flogging because that would not have been considered among the "cruel and unusual punishments" banned by the 8th Amendment at the time of its ratification. Instead, we should look for the plain, present, public meaning of those constitutional terms. We--and not the long-dead founders--face the lash. therefore our consent--or lack thereof--should control.
(Justification does rely on consent, by the way, but the relationship is not a black-and-white one. See, Graduated Consent in Contract and Tort Law: Toward a Theory of Justification, 61 Case Western L. Rev. 17 (2010). If you're in a rush, you can find a slightly earlier version, download-ready, here.