The answer above is completely incorrect. The actual answer is going to be the second option: They shared the belief that rights granted by the US Constitution should apply to all Americans. Hope it helps.
This is quite difficult to answer since the puritans were persons who had very strict moral values and i can't find an answer to correspond with the definition.
My reaction to this quote is that Abraham Lincoln is referring to the ideal that once people have power they tend to abuse it for their advantage, and personal gain. For Example, gerrymandering. Gerrymandering is the manipulation of the county sizing and grouping in states by the Legislative branch to guarantee their reelection into federal or state offices. A typically Democratic city perhaps may be grouped or redrawn to conjoin with a vastly Republican populated area, creating a larger group of supporters of one party, and a polarized county.