It's hard for me to see how a taxi would be much faster than the Orange Line, and at that time of day you really might get delayed one way or another in a vehicle.
You could maybe shave a few minutes off hindukid's method by taking a cab for the last bit. My guess is that best would be MDW-Roosevelt (online scheduler says 21 minutes) and then about 8-10 minutes once you grab a cab (one block east and then less than 3 miles N). If traffic is not bad, cabs drive fast.
Don't forget that you might have to wait a few minutes at MDW for the Orange Line and it takes a couple minutes to walk there.
Sounds like The Amazing Race!