"Your bad".... NOT!
I'm puzzled why the 60 * 1000 didn't work but passed (I presume?) the compiler's validity tests, and would welcome claification on that point.
And even though it wasn't the answer to what you were seeing, I'd welcome what you suggested. If someone who knows the answer would modify the entry at....
http://www.arduino.cc/en/Reference/Delay
... to make explicit what the largest acceptable arguement is, I think it would be a good addition. The entries for miilis and pulseIn are very good in this respect. It would be great if the explicit statement of different functions needs were to be extended.