At what point can I start playing against the bosses in Naxxramas successfully?

I used this deck to defeat the first 6 normal mode bosses. This deck won against each boss on the first or second attempt (many times in close contests).

Mage

Arcane Missiles
Ice Lance x2
Elven Archer x2
Mana Wyrm
Frostbolt x2
Amani Berserker
Kolbold Geomancer x2
Millhouse Manastorm  (Legendary)
Arcane Intellect x2
Frost Nova x2
Mirror Entity
Cone of Cold x2
Polymorph
Water Elemental x2
Azure Drake x2  (rare)
Stampeding Kodo  (rare)
Archmage
Frost Elemental x2
Reckless Rocketeer
Ravenholdt Assassin  (rare)

There are four rares and one legendary. Millhouse is just for fun and a Raptor will do in his place. The Ravenholdt could be an ogre or golem. Replacement for the Kodo is unclear, but you're looking for a nice two for one card. Replacement for Azure Drake could be Gnomish Explorer.

To answer your question: if you've opened enough packs to have a few rare cards, I'd say you are well prepared for Naxx normal mode.

Update: I've gotten through Patchwerk with this deck so far. Some fights are very difficult with it and a matter of playing until the right cards come up.

I've found priest and ice mage to be good in most of the normal-mode boss fights. Once you beat Maexxna and get the Nerubian Egg, a buff pally decks is also strong. Some things to keep in mind that are different from matches vs other people:

1) Most of the bosses have an initial board state advantage. You will probably need a lower mana curve than normal to neutralize this threat quickly.

2) Make sure to include 2* Acidic Swamp Ooze against bosses with strong weapons.

3) Some of the bosses have weaknesses that you can use to your advantage. For example: Ex - Maexxna

Maexxna will ALWAYS start off the turn by using its hero power, even if it is a strategically bad move. You can take advantage of this by adding a lot of low-cost Battlecry minions to your deck.

Ex - Loatheb:

Include low-cost Charge minions in your deck, and cast them before killing Spores. Now you have Charge minions with 10+ attack.