A lot of people think that TR would have gotten the US into the Great War earlier but I am a bit skeptical about that. 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. TR himself wrote--admittedly before the *Lusitania* sinking--"I ask those individuals who think of me as a firebrand to remember that during the seven and a half years I was President not a shot was fired at any soldier of a hostile nation by any American soldier or sailor, and there was not so much as a threat of war. Even when the state of Panama threw off the alien yoke of Colombia and when this nation, acting as was its manifest duty, by recognizing Panama as an independent state stood for the right of the governed to govern themselves on the Isthmus, as well as for justice and humanity, there was not a shot fired by any of our people at any Colombian. The blood recently shed at Vera Cruz, like the unpunished wrongs recently committed on our people in Mexico, had no parallel during my administration..."
http://books.google.com/books?id=_VMyAQAAIAAJ&pg=PA134
Obviously, TR is not going to say America is "too proud to fight." But I don't think he will ask for an immediate declaration of war, either--which I doubt he could get through Congress even after the Lusitania sinking. He will probably put much more emphasis on "preparedness" than Wilson did (Wilson was a late and only a partial convert to that cause), in the hope that building up an American military stronger than that of of OTL in 1914-17--and readier to get to Europe within a reasonable time--will dissuade the Germans from resorting to unrestricted submarine warfare. (Of course, here too he might have some trouble getting Congress to agree.)