The DirecTV site does not make you enter a SSN to sign up, but without it you will have to pay a deposit.
I would just pay the deposit, because even if you go though the trouble of getting a non work eligible SSN you won't have any US credit and they'll charge you a deposit anyway.
BTW, the Walmart Money Card REQUIRES a SSN to make it reloadable. Most of the major "Re-loadable" cards require them because they are practically considered bank accounts and have routing/account numbers associated with them.
You're going to need to get a pre paid gift card, most of them max at $100 but I think I've seen some that go to $500. You could initially get the walmart money card, you'll be able to use the balance of what you initially put on it but won't be able to reload without giving SSN to order a permanent pressed card.
As for a US phone number for the account,
http://voice.google.com
So when you come to the US, sign up online without giving SSN and pay the $300 ish deposit with a pre paid card.
As far as ongoing payments, I would try using your Canadian card to pay it and say a friend in Canada is paying the bill if there is a problem.