Hmmm... Stanley Fish says that it's impossible to be a "strict constructionist" without imputing some sort of intention to the words of the Constitution, as Scalia wants to do. Ramesh Ponnuru says no, you can:

Scalia's point, I take it, is that if we want to know the meaning of, say, the First Amendment, knowing the Framers' views about religious freedom does not settle the matter. The illustration usually brought up here is that if a secret letter from James Madison saying "what we had in mind was to prevent our new Congress from hiring chaplains," it wouldn’t matter. What matters is what the ratifying public of the time understood the words of the amendment to mean.

Okay, but… I'm very far from an expert on constitutional history, but as far as I can tell, several scholars have pointed out that, for instance, the Civil War amendments were very likely kept purposefully vague so as to attract broad support. (Eric Foner is big on this idea.) In that sense, if different parts of the "ratifying public of the time" took words like "freedom" to mean different things, the Scalia project is quite shot. I highly doubt the ratifying public—even if it has been a small minority within the larger public—all agreed on what the words of various amendments meant. But that aside, if it was in fact the framers' intention to keep certain language vague and leave it to future generations to adapt for their own purposes, Scalia would be pretty clearly working against the spirit of the whole enterprise. How do you get around this? It's much harder to dismiss this sort of intention than the "secret letter" Ponnuru is talking about.