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I have achieved relative invincibility pretty quick with this affinity build. Usually get platinum angel out pretty quick (and wait till my opponent it tapped out if blue) so countering isn't a huge problem and haven't had an issue with sacrificing because there are so many cheap creatures. Then you just wait to either get milled down or draw yourself out before dropping psychic spirals for the win.
http://www.mtgvault.com/avatarofwhoa/decks/challenge-invincible/

Dunno if either of these are COMPLETE invincibility, but I've managed to win several times with both of these "no, don't touch me" style decks. My Red Tape is one of my favorite because all the names of the cards work within the theme too (lordy, that was difficult, haha) and I also noticed a combo I wasn't planning on... Solitary Confinement has you have no draw step and discard cards to keep it going... Walking Archive has you draw cards on UPKEEP.
http://www.mtgvault.com/axiluvia/decks/red-tape-v2/

This one is amusing because most of the spells are "I won't bother with your stuff unless you use it on me". Also Swans of Byrn Argoll + Entangler = hilarious when they realize they're going to deck themselves by attacking. Or Pariah on them. Or both.
http://www.mtgvault.com/axiluvia/decks/hold-back-v2/