Its a chainring/chain issue NOT a spindle length issue.
In my years of wrenching I've found there to 2 primary reasons for this:
1: Chainring are too far apart due to either too many spacers or the rings being bent out. In this particular instance its not a spacer isue but the large ring could be uniformly bent out or flared so to speak. Its unlikely the small ring is unifirmly bent towards the seat tube. As Kurt mentioned its spinning because its not engaging due to the wide space between rings.
2: The chain. Just because a chain says 6/7 whatever on the box doesnt mean it'll work. 6/7/8/9 whatever simply refers to chain dimensions not neccessarly compatibility.
Changing the spidle will NOT fix this. How many of you have seen a chain ride on top and spin on a freewheel cog? It happens.....