One interesting aspect of American politics is the 2.5 month period between a presidential election and the swearing in of the new president. The swearing-at the incoming president happens right away, but we have an awkward period where the incoming president has no direct power and the outgoing president has lessened power, left to make trips abroad and contemplate any last-minute pardons or administrative decisions that could advance his side's cause or his legacy.
In contrast, the transition period in parliamentary systems takes hours rather than months. The day after a British election, the old PM has his stuff hauled out of 10 Downing, he goes to the Queen to tender his resignation, the new PM goes to the castle to be formally asked by the Queen to take over, and the new PM's stuff gets hauled into 10 Downing. There is no lame-duck period to speak of.
President Obama has been rather gracious, publicly hoping for the best from the new administration and assuring the rest of the world that Trump isn't quite the Devil incarnate. His professorial style can come off as condescending if you're on the wrong end of an issue, but that aloofness seems to help take some of the steam out of the frustration of the left.