I suggested once in soc.history.what-if that Wilson could beat either Taft or TR in a one-on-one race in 1912.
https://groups.google.com/d/msg/soc.history.what-if/NZXQky_Jgpk/OhWnTSyjfwoJ But that was contingent on a bitter struggle between Taft and TR for the GOP nomination, as in OTL--my point was that whichever one won, a lot of the backers of the loser will not back the nominee in November. I specifically stated: "It might seem that TR, not associated with the Taft administration's unpopularity, might stand a better chance against Wilson in a two-man race. But here it is important to note that it matters just *how* TR gets the Republican nomination. If Taft suddenly announces in 1910 that he will retire in 1912 and suggests that TR should get the nomination; if TR then gets the nomination by maneuvering adroitly between the progressives and conservatives in the GOP, as he had done as president--if all these things happened, yes, TR might have won the general election. But this was not going to happen. Taft was not going to 'go quietly.' The only way for TR to get the nomination was in a hard-fought anti-Taft campaign..."
Obviously, if health considerations prevented Taft form running again, and he announces that at a fairly early time, there will be much less bitterness among Republicans--and TR will probably run on a less radical and less controversial platform than he did as a contender in OTL. There will of course still be objections to the "third cup of coffee", but overall I would say that TR would have good chances of winning in November. Even then, I wouldn't be
sure about it, though, after all, the Democrats had won the House in 1910,
before the Taft-TR split.
Assuming TR wins, does the US enter the World War early? TR in OTL certainly *talked* belligerently as a critic of Wilson. TR said that after the sinking of the Lusitania, had he been president he "would have seized every German ship docked in the United States, telling Berlin: 'Now we will discuss not what you will give but what we will give back.' In late October he told a Denver audience that, if necessary, he would have gone to war over the matter. The slogan 'He kept us out of war' Roosevelt branded 'the phrase of a coward.'"
https://books.google.com/books?id=iyfEIkl3hXcC&pg=PA212 [1]
And yet...it is after all easier to talk that way if you are not president. As Henry Pringle, biographer of both TR and Taft, once noted:
"In 1886, Theodore Roosevelt had hoped for war with Mexico. In 1896, he considered the possibility of sanguinary combat against William Jennings Bryan and his fellow Populists. In 1898, he agitated for war with Spain. In 1911, he volunteered to fight against Mexico. In October, 1914, he said that the United States should uphold the neutrality of Belgium. It will be noted, however, that not one of all these belligerent expressions was voiced between September, 1901 and March, 1909. It was one thing to urge that some other president involve the nation in blood. It was a far different thing to face the responsibility himself." *The Life and Times of William Howard Taft*, p. 296.
So it is not really clear to me that even if TR would have been president in 1915 the US would have gone to war at that time.
[1] Needless to say, the Democrats made good use of TR's belligerent rhetoric. A November 4 advertisement from the Wilson Business Man's League:
***
"You Are Working--*Not Fighting*!
Alive and Happy--*Not Cannon Fodder*!
Wilson and Peace with Honor
or
Hughes with Roosevelt and War?
Roosevelt says we should hang our heads in shame because we are not at *war* with Germany in behalf of Belgium! Roosevelt says that following the sinking of the Lusitania he would have foregone diplomacy and seized every ship in our ports flying the German flag! That would have meant *war*!
Hughes Says He and Roosevelt are in Complete Accord!
The Lesson is Plain:
If You Want War, vote for HUGHES!
If You Want Peace with Honor, vote for WILSON!"
***
No wonder the German ambassador Bernstorff told Berlin "If Hughes should be defeated he can thank Roosevelt."
https://books.google.com/books?id=RFgLAAAAYAAJ&pg=PA297