Investigators say 48-year-old David Lee Simpson, of Bath, N.Y., also threatened an Arizona woman. He has pleaded not guilty.
Court records show the trial was set for April 1 after a hearing in the case Thursday.
Authorities say Simpson was in New York when he sent the tweets, but Arizona asserted jurisdiction since the threats were made against individuals for conduct during their coverage of a case that was occurring in Maricopa County. Authorities say both TV personalities -- Nancy Grace and Jane Velez-Mitchell -- were in Arizona at times.
The two are hosts on Turner Broadcasting's HLN network who covered the Arias trial.