There are two important ideas in this quote.
First, that the Constitution is inspired. This isn't just the opinion of Brother Taylor. It's cannonized scripture, though it's not an often quote couple of verses. When I first began to study liberty, I was quite surprised to find that the Constitution has place in the scriptures, even though I'd been a member all my life, attended Sunday School, completed Seminary, and gone on to Institute where I had learned a ton from a great teacher. But look:
The Constitution comes to us from the Lord. It is one of His tender mercies, designed to safeguard our agency. The battle for our agency may have began in the pre-earth life, but it rages still today.
And for this purpose have I established the Constitution of this land, by the hands of wise men whom I raised up unto this very purpose, and redeemed the land by the shedding of blood.
-Doctrine and Covenants 101:80
The second important idea is that only strict observance of Constitutional law can keep our nation safe. Before we can strictly observe the law, we must know the Constitution. What it actually says. The reasons why the Founders wrote what they wrote in it. We need to educate ourselves, because most of us didn't learn it in school, and we need to educate our children, because they certainly aren't going to learn much, if anything, about Constitutional limits and principles from schools run by a government that observes no limits to its power. If we want to know, we'll have to search out the information for ourselves. We must want freedom enough to inconvenience ourselves in order to learn how to be free.