Forgive my shameless self promotion, but last night I've placed Baxter's Venture: Director's cut on Greenlight.
http://steamcommunity.com/sharedfiles/filedetails/?id=274636766
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While this game is waiting to be Greenlit (no time to determine how long) I'm currently replay-retesting to make sure I've nailed the bugs, reworking the save/load function. It will be exported via node-webkit. I'm not sure if it's mandatory to use Steam's API I don't know how all that works since this is my first game uploaded on their site.
I've read some games get greenlit in a matter of days, some weeks, months even. From my understanding if your games pass muster it's just random. I do believe having a good number of Yes votes determines how fast it goes I think.