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FUN FACTS:
United States Code Title 18, Section 871 states it is a felony to make "any threat to take the life of, to kidnap, or to inflict bodily harm upon the president of the United States ".
Title 18, Section 3056 gives Secret Service agents the right to make arrests without warrants "for any offense against the United States committed in their presence, or for any felony recognizable under the laws of the United States if they have reasonable grounds to believe that the person to be arrested has committed such felony.".
So, the second that person confirms they made that tweet, they can arrest them and immediately search the home. Their best bet is to refrain from any communication until legal representation is present. So it really should have been "Hi we're here about your tweet about Trump". "I have nothing to say until my lawyer is present".