It would be generally fairly difficult to call President Obama a nationalist. If anything, he has been criticized roundly for not being sufficiently nationalist. The Republicans have denounced what they call his “apology tour” because they say he did not stand up enough for the United States. They denounced him for saying that the US is a special country but that the people of other countries typically think their countries are special as well.
If we are to say that Obama is a nationalist, we would need to look at things like his statements about China. Obama has, at times, taken a fairly tough line on China. He has tried to use things like statements about their trade practices to make it look as if he is being aggressive towards them. He has also embarked on a well-publicized “pivot” towards Asia to try to put the US in a more powerful position in that region.
On the whole, though, President Obama has not seemed nearly as nationalistic as many other presidents have been.