The line was drawn some 225 years ago: The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
It's not about drawing the line, it's about holding an uncooperative government to it. They're willing to go so far as shoot you if you don't let them cross that line and examine your coffee; you're not willing to pursue similar means to hold them to that line.
Some states are considered to lie completely within a "constitution-free zone": Connecticut, Delaware, Florida, Hawaii, Maine, Massachusetts, Michigan, New Hampshire, New Jersey, New York, Rhode Island and Vermont.
Well, by the ACLU. They describe what they mean in the fact sheet linked from the page that was provided:
The border, however, has always been an exception. There, the longstanding view is that the normal rules do not apply. For example the authorities do not need a warrant or probable cause to conduct a “routine search.”
But what is “the border”? According to the government, it is a 100-mile wide strip that wraps around the “external boundary” of the <?XML:NAMESPACE PREFIX = ST1 />United States.
(I left the XML error in there just for the lulz.)
You can disagree with their analysis, but it's pretty clear that their position is that normal 4th amendment rules are being superseded merely because of a rather wide proximity to the border.
It's not about drawing the line, it's about holding an uncooperative government to it. They're willing to go so far as shoot you if you don't let them cross that line and examine your coffee; you're not willing to pursue similar means to hold them to that line.