Michael Jackson probably said it in the 80's when he watched the Ullman shorts. "HEEE! I'd really like to do the Bartman. SHAMON! CHA! C'mon Bubbles, let's invite some kid that looks like him to a sleepover. AHHHHHHHHHHHHHHHH!"
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Way too damn early to be doing the Bartman in 83. I think Bartman came out in the early 90's.

This is obvious if you think about it.
"Do the" is a direct reference to the 1978 film Dawn Of The Dead but with the first two words abbreviated (he doesn't want to give the game away to Nancy). Instead of "Dead" Steve replaces it with "BARTMAN" (which really should be capitalised) and goes back to the full acronym style and stands for "Barb, Arisen Reborn, Trans-dimensional Monstrous And Nasty".
Steve is actually in league with Brenner (they met as they share a hair stylist - which should be fairly clear to everyone) and he's providing the Demogorgon with hosts to procreate. So he knows Barb is about start the transformation process.
This is exactly why he appeared to do more damage with a bat with nails in it than a room full of armed goons. It was all staged between him and the Demogorgon, sure he looked surprised in the Byers but would you really run back into that house unarmed - think about it.
As an aside Steve's government contacts soon have him moving through the ranks of connected people, which is why in a few years he's working on the Tracy Ullman Show, where he plants the idea for Bart and then later the Bartman as a sick and twisted reminder of his night with Nancy.

Not in 1983, that's for darn sure.