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Perhaps covfefe is a verb, and the sentence is imperative, directed at the press, and “Despite the negative” is a subordinate clause, and “press” is part of a classical apostrophe, like “O happy dagger.”
In that case, perhaps we can understand the tweet to mean “Despite the negative [things I tweet about you] [, O members of the press,] covfefe.”
And if that is true, then perhaps we can interpret “covfefe” as an exhortation for the members of the press to keep doing what they are dong.
“My hands are not small.”
“I am still in charge.”