Jack Balkin argues that originalism is consistent with a living Constitution, in a very interesting way. See the summary by Randy Barnett, and read the whole paper (follow the links from Barnett's post) if you want to look at the details.
Once you distinguish between original meaning and original application, you can say you're an originalist about original meaning but not original application. The terms of the Constitution mean what they originally meant, but how that is applied in new contexts will change. An example would be that the original application of the equal protection clause obviously did not include things like affirmative action because the people who authored it did not see that language applying to such things (see here for why), while the language itself may actually have implied something that its authors wouldn't have wanted to apply it to. So the living Constitution is when the applications change.
This strikes me as along the same lines as what Justice Alito was saying at his hearings back when he was still Judge Alito. I'm not sure if it's Alito's own view, but it's interesting to see Balkin willing to adopt a form of originalism, since he has been a strong critic of the kinds of originalism that Justices Scalia and Thomas hold (which are distinct from this kind). One irony of this is that the affirmative action discussion I just linked to doesn't follow from this new form of originalism that Balkin has identified. Balkin's argument against the Scalia-Thomas-Rehnquist view of affirmative action is that the original application of equal protection does not include things like what affirmative action now is. But of course that's irrelevant if original application isn't what determines the meaning of constitutional language.