The most plausible POD for this is that TR does not make his famous OTL Election Night statement of 1904. ("On the 4th of March next I shall have served three and a half years and this three and a half years constitutes my first term. The wise custom which limits the President to two terms regards the substance and not the form, and under no circumstances will I be a candidate for or accept another nomination.") Then in 1908 he says he is running for his "second elective term" but rules out future terms. My guess is that, as in 1901-8 he manages to paper over the differences between progressive and conservative Republicans. The GOP will suffer some losses in 1910--after that many years in power, a there is bound to be some wear and tear--but nothing like the 1910 of OTL, where Democrats actually won control of the House. The GOP is not guaranteed victory in 1912, but at least will be fairly united and in better shape than in OTL. The question is who the GOP nominates in 1912. Taft would be an obvious answer, except that it is very likely he would want to be appointed Chief Justice after Fuller died in 1910. TR would probably like Root, but would realize that his image as a conservative "Wall Street lawyer" would hurt the GOP in the Midwest and West. Hughes may be the best choice in terms of electability, but TR never seemed to care much for him. The GOP convention, in its heart, would probably prefer a conservative like Fairbanks, but that would IMO give the Democrats a real chance even against a united Republican Party...Maybe, seeing this, TR decides after all to accept a "genuine draft" by the party?