Depends on source. Can end up being a 30 min taxi or a 90 minute public transit if you live somewhere not handy to the blue line (say, Rogers Park to Ohare)
There are ways to carry your bags on the train. Many tourist travelers have no clue and should be punished for it. (I.e. using them to block the aisles during rush hour, blocking areas of the train etc)
They do, they don't even look sympathetic about it. That's the worst part.
I ended up just berating a family coming back from an Emirates flight who just lined their luggage in the aisle from the back to the door and the back part of the train. They sat in the first few rows of the car. (they left rows of seats open, blocked, and I was blocked in at the back)
Lets just say. At that point of time, I didn't start with niceities the stop before I got off.
Honestly, you have that amount of luggage, take a cab or some sort of airport bus that is setup for people with luggage. Yeah, that family was obnoxious (or at least clueless) but crowded subways and commuter-type trains aren't intended for people with more than light carryons at most. (And even those can be a pain during rush hour.)
In traffic probably, if you have lots of bags and its not rush-hour or you aren't close to the train/in a suburb where you'd have to go downtown first then a car is much easier/faster.