Hard to top Washington-Adams-Jefferson-Madison-Monroe. Hell I'd even extend that to Washington-Adams-Jefferson-Madison-Monroe-JQA-Jackson.
JFK wasn't a particularly good President. His legacy punches far above his accomplishments because he was a young, handsome playboy who got assassinated.
Madison's presidency was defined entirely by starting an unnecessary war and then losing that war. It was a miserable failure from any ideological perspective and easily breaks that streak no matter what criteria you're judging the presidents on.
The war was completely necessary and justified - every peaceful means to get the British to respect our rights had been attempted and exhausted - and for America's intents and purposes it was a victory. America spent the 40 years before the War of 1812 desperately trying to preserve its sovereignty amidst the great power struggles of Europe. After that war, our sovereignty was no longer at risk, and our equal status as an independent nation was firmly established. Mission accomplished.
The War of 1812 was not a win by the standards the War Hawks set in 1812 (humiliate Britain and get a chunk of Canada). It was a win in the sense that the US still survived territorially intact, but that was only the standard after the British burned our capitol down.
Anyway the US was way, way too weak to go against Britain at that point and the War Hawks were insane to insist on this war. I also think the Federalists who wanted us to fight France in 1798 were similarly insane (perhaps more), for what it's worth