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1.
To get belligerently intoxicated. Involves chiefly the consumption of brown liquor in the form of shots. After morning effects include the occasional induced upchuck and having your skin "reeking" of booze. Actions often include incoherent yelling, mindless babble and aggressive, unsuccessful advances to members of the opposite sex.

And yes, it is a mild reference to the alcoholic tendencies of our friends on the reservations.
"I am throwing down the hammer tonight - by 11 will assuredly be Indian Drunk."

"Wow, that girl is falling over and slurring her words. A solid Indian Drunk."

"I was so Indian Drunk last night I lost my keys, bought 20 lap dances for people I don't even know and called every girl in my phone at 6 AM."
by WiggyLuckles December 11, 2006