(verb) "visit someone to get political support or find out opinions"
The modern sense began to appear in the 16th century. Shakespeare uses the word twice, and neither time do the modern meanings work. In Henry VI Part 1 (I.iii.36), Gloucester harangues Winchester: "I'll canvass thee in thy broad cardinal's hatIf thou proceed in this thy insolence." He is evidently not asking for votes. Here, the meaning is an older one, now obsolete. The verb came into the language in the early 1500s as a development of the noun canvas: "toss someone in a canvas." It could originally have been either for fun or for punishment, but by the end of the century it predominantly meant "knock about, thrash, batter". As so often in Shakespeare, hints about the meaning of an obscure word can be found in the context. So, in Henry IV Part 2 (II.iv.217), Falstaff curses the swaggering Pistol: "A rascally slave! I will toss the rogue in a blanket", and Doll Tearsheet replies, "Do, an thou darest for thy heart. An thou dost, I'll canvass thee between a pair of sheets."