oil wont really hurt the cooling system, but neither was the cooling system intended to have oil in it... if you flush it with a good product intended for the purpose and according to directions, it will be fine.
if you dont get to it immediately, it isnt going to cause any problems other than it may smell as the temp comes up...
if you do need to make a trip or two before you get around to flushing it, keep an eye on the temp gauge, as oil in the system does cause a slight loss of efficiency as oil does not carry heat away as fast as water, but unless you have another unknown problem you should have plenty enough cooling capacity that the small amount of oil wont make any difference.