It is in the bible in a variety of different ways. John is not off his rocker on Christianity. He did pick an unusual setting, though. That might bite him. But he’s right about Christian interpretation, though.
But he was referring to a Jewish tradition, identifying the house as having sacrificed their own personal lamb, the choicest male belonging to the house hold (sometimes more of a pet than just livestock) with proof of the sacrifice identified by the smearing of the blood. We aren’t ignorant of the Bible, sir, and his interpretation as believed most popularly by a small section of Christians has no place in this conversation about the Jewish tradition. I have nothing more to say on this.
You are, of course, correct. I am surprised by how many people who would otherwise identify themselves as Christians apparently don't understand the Messianic typology of the Passover lamb. This is a paint-by-numbers stuff -- what do they think John the Baptist meant? (i.e., John 1:29) -- even if (attempted) Kasich's expression of it was rather poorly done in this instance.
And, as you say, the setting in which he related it was, on its face, rather "provocative." If Kasich actually intended it as such, I'd have to give him credit (although I don't know how he thought do so would help him politically); if he was being inadvertently impolitic, well, then, Kasich was, in his own way, as off-base as Trump's referring to "Second Corinthians" as "Two Corinthians" during his speech a few months back at Liberty University.