I’m from Ireland and always thought it meant “tough luck, deal with it”
In the USA it seems to mean 'cope' or put up with.
In Australia / UK it means do something about it.
"You should deal with it / I'll deal with it" - do something to solve the problem
"Yeah, deal with it!" - dismissively, put up with it
I don't know if the latter came from the American usage, but I certainly hear it used.
With an unspecified subject "deal with it", it does mean "put up with" or abide. However, if your boss told you that "We haven't been paid yet; deal with it!", odds are good that you're expected to be on the phone or otherwise chasing down the tardy clients.
The only thing that came to mind is "bite/eat it" (i.e., fall), and there "it" is presumably the dirt/snow/pavement/etc that the person fell onto. The "it" in "hit it" and "cool it" seems to refer to the on-going action/attitude too, even if it's not precisely specified.
If you're curious about dummy objects, there is a short list of examples on wikipedia ( https://en.wikipedia.org/wiki/Dummy_pronoun#Dummy_objects ), such as make it [achieve success].
Taking more examples from your link:
- "I don't get it" == "I don't understand [something]", in the same way that "I don't get math" == "I don't understand math."
- "He made it" == "He succeeded [generally]", but you can drop in several concrete goals: "He made the team/grade/partner" == "He was successful at ..."
- "Deal with the problem" == "Take some action to solve the problem", but "Deal with it" == "Abide the current situation because it will not change".
As other comments have pointed out, there is no difference in meaning by country. Both meanings exist, and which one is being used is determined by context.