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I don't think the Lincoln "team of rivals" analogy takes you very far.
Lincoln's cabinet was stacked with heavyweight contenders, in part, because Lincoln himself was widely considered a feather weight, hackneyed compromise candidate and both the party and the establishment of the time would not have allowed him to surround himself with anyone else. Once in office, the rivalry did not save Lincoln's bacon during the Civil War. Grant and Sherman did that. Lincoln was in way over his head in 1861, spending as much time on postal patronage appointments as affairs of state; he was consumed with McClellan's misadventures in 1862; and it was not until the war showed some signs of progress in 1863 that he gained firm control over both his military leadership and his cabinet. Men like Seward were of course important to the cause, but I'm not sure what lessons the "rivalry" contains for 21st century governance. By the way, McClellan was a "rival" too, from the time he was serving as army major general, yet he ended up breaking out and running against Lincoln. Some rivalries may be more equally pendantic than others.
I suppose you could say the Hillary Clinton . . . whatever it is going on right now . . . relates to rivalry, to the extent she and Mr. Obama are once and (possibly) future rivals. But I don't see much application to Lincoln beyond that.