From what Lincoln said in the Gettysburg Address, he seemed to think that the divided house that could not stand occurred when one side left. I think the house divided that will not stand is when you have two large factions within the same country that have mutually exclusive visions for governing that country.
The phrase is not from the Gettysburg Address.
It is from a speech Lincoln gave in June, 1858 when he accepted the nomination of the Republican Party for Senator from Illinois.
The phrase is actually a quotation from the Bible, from Matthew 12:25.(See also Luke 11:17): “And knowing their thoughts He said to them, “ Any kingdom divided against itself is laid waste; and any city or house divided against itself shall not stand.”
He used it in the context of a country heading toward a crisis because it was half slave and half free, and he believed that it would soon become all one or the other, but it could not stay as both.
His words were very prophetic.
I think we both see today as the two visions of what America is, from the traditional right to the radical left, cannot always exist together.
One will have to win out over the other.
No man is good enough to govern another man without that other's consent. Any people whatsoever have the right to abolish the existing government, and form a new one that suits them better.
This is a most valuable, a most sacred right.'
--Abraham Lincoln, 1848
Omnium consensus capax imperii nisi imperasset"
-Tacitus
[Everyone would have thought him fit to rule, if only he never had.]