Well, there were some supremely important things they all agreed on.
Just to name a few:
That our rights come from God, not from any man.
That the reason for being of government is to equally protect the aforesaid rights.
That those rights preceded and supersede any written document or man-made law.
That our Constitution is the expression and the instrument of the people, who are sovereign under God.
And so, the answer to the question at the top of this thread, "What If the Government Rejects the Constitution?" is, throw out the officers of government and start anew with those who will respect our rights, the sovereignty of the people, and the authority of the Constitution.
And I agree.
I merely point out that Jefferson's "strict construction" theory was one of two positions taken by the Founders. The conservatives were Federalists.