WASHINGTON—President Trump isn’t expected to declare a national emergency at the southern border when he addresses the nation Tuesday night about his request for funding for his long-promised wall along the U.S.-Mexico boundary, according to a person who has reviewed drafts of the speech. The president’s speech didn’t include any declaration of a national emergency, according to the person. Instead, the speech seeks to explain the president’s rationale for why he viewed the situation at the border as a crisis. Mr. Trump has said he wouldn’t sign any bill ending the partial government shutdown, which is now in its third...