Minimum National Swing Needed for a Losing Candidate to Win

[True Federalist (진정한 연방 주의자)]

1968:

Hubert Humphrey 43.9% 246 EV*
Richard Nixon 42.3% 247 EV
George Wallace 13.5% 45 EV

*Assuming that Southern Democrats in the House ultimately vote for Humphrey

Alternatively,

Hubert Humphrey 44.2% 275 EV
Richard Nixon 42.0% 218 EV
George Wallace 13.5% 45 EV

Southern Dems voting for Humphrey was no sure thing.  However, if Nixon kept his end of the bargain he struck with Humphrey, it wouldn't matter.

[True Federalist (진정한 연방 주의자)]

What exactly was the bargain between Nixon and Humphrey?

Allegedly, that if one of them won a plurality of the Electoral College, but not a majority, the second place person would see to it that enough of his electors either did not cast ballots or voted for the first place ticket to keep the election out of the House so that neither side would need to make a bargain with Wallace and his allies.

[True Federalist (진정한 연방 주의자)]

Silver was largely a spent issue by 1908 and the West was where Debs did best.

Green 30 to 80 % = Debs 3 to 8%
Yellow 30 to 50% = Debs 0 to 2%
Grey = Debs not on the ballot

[True Federalist (진정한 연방 주의자)]

Here is a map of the House delegations in 1860 under the lame duck 36th Congress.

For ease of computation, I assigned all Democrats in the slave States to the Southern Democrats and all the free States to the Northern Democrats, tho that might not be the case, especially for California and Oregon.

Republican - 15
Southern Democrats - 12
Northern Democrats - 3
American (i.e., southern Whigs; known as the Opposition Party in some states) - 1
Split Southern Democrats/American - 2

Since the Senate is solidly Democratic, whoever is not Hamlin out of the two choices they get will be Vice President and thus Acting President if the House deadlocks.

There's zero chance that Lincoln can get the needed 17 delegations in the House, and with either Sen. Lane (SD-Oregon) or Gov. Johnson (ND-North Carolina) elected Vice President by the Senate, I think the Republicans would likely support Douglas or Bell as the lesser of two evils versus Breckenridge or the Vice President.

However, if Everett (CU-Massachusetts) were Vice President, there might well be a deadlock in the House.  The Republicans would likely prefer Everett to any of Douglas, Breckenridge, or Bell, so they likely wouldn't vote for anyone except Lincoln.  While the Democrats would only have one dog in the running the CU came in second in the electoral college, it wouldn't be enough to elect a President unless they could unite with the American Party, which seems most unlikely unless they get together to elect John Bell of Tennessee.

Anyway, with all that as precursor, how about having the Bell/Everett ticket do well to get second, with no one getting a majority?

[True Federalist (진정한 연방 주의자)]

So you want a scenario where the House must decide between Lincoln/Douglas/Bell instead of Lincoln/Douglas/Breckinridge? IIRC, the House can only decide between the top three candidates, so Bell isn't an option in the current deadlocked scenario.

Yup.  Lincoln/Breckenridge/Bell would also be interesting.  While not a minimum swing by any means, here is an example of a double swing involving swings within the fractured Whig and Democratic parties. (Not a uniform swing, the swing shown is 20% of Lincoln votes to Bell and 20% of Breckenridge votes to Douglas, even in states where Bell or Douglas were not on the ballot.)

109 EV 33.2% PV Douglas
  83 EV 31.7% PV Lincoln
  73 EV 20.5% PV Bell
  38 EV 14.6% PV Breckenridge