Edit: This post turned out a lot longer than I intended!
I’ve expressed my feelings about Donald Trump many times on this site, and the fact that my dislike for him extends back a couple decades, long before he ever publicly expression any political aspirations. That being said, I will make an attempt at objectivity, difficult as that may be.
Donald Trump is a master of marketing and media manipulation management, with no experience in government or politics. His marketing savvy turned the election into a contest based on public appearance rather than public performance or experience. When he accused the news media of bias, for example most took it to be a complaint; few realized how skillfully he and his organization were manipulating that bias to his advantage.
And when he publicly alleged that the voting system was rigged, few realized that he was bragging rather than complaining. He used weaknesses in the system to his advantage.
He is shrewd enough to know that anything repeated loudly enough and often enough into the public ear will take on the appearance of truth, whether supported by facts or not. He used this to his advantage when attacking his opponents’ character. This was especially effective against Hillary Clinton. Here public persona had been attacked since the days when she was First Lady, and it seems the accusations never stopped. So his use of the pejorative “Evil Hillary” was more than mere name-calling; it was a calculated insertion of the term into the “echo chamber” known as the news media.
So now to answer the OP…
Any speculation on the point will be biased by the speculator’s view of history. But I will still try to be objective.
Although Barack Obama does not have the years of accusations, investigations, and castigations that Hillary brought with her, there are several other things in his resume that could be used; for example, there have been innuendos about his birth, his “Muslim” connections, his “Chicago mob” associations”, and probably several others areas that could be exploited to Trump’s benefit.
It would be difficult, but if Obama could somehow keep the conversation on qualifications, I think he could do it .