I'm reading this article and I do not understand why the bolded を exists. I'm am expecting a verb such as する, but there isn't one. How is the を functioning here or why is there no verb paired with it?
アメリカのトランプ大統領は、自分のことを悪く書く新聞やテレビを「うそのニュース」や「国民の敵」だと言っています。
My Translation: American president Trump says that things like news papers and TV who write poorly about his matters are "Fake News".
No verb? Isn't 「言っています」 a verb (phrase)?
「Person + は + Object/Another Person + を/のことを + "Name" + と/だと/って + 言う/言っている, etc.」
is an extremely common expression meaning:
"(Person) calls/is calling (Object/Another Person) "(Name)"."
「言う」 means "to call" in this expression and you will keep encountering this construct for as long as you study Japanese.
"U.S. President Trump calls the newspapers and TV (stations) that speak ill of him 'Fake News' or 'enemies of the people'."
The verb is だ, not 言う.
テレビを「敵」だと大統領は言う。
The president says that the TV is the enemy.
You can replace を with が:
テレビが「敵」だと大統領は言う。
テレビが「敵」だ(the TV is the enemy) is one sentence with だ as a verb.
大統領は言う(the president says) is another sentence.
