I'm glad I read this thread!! So if I show up for a US flight from PHX with a set of golf clubs and by the time I get to the ticket counter (wait in line etc.) it is now 40 minutes prior to my flight they won't let me fly?!?!?

Clearly I can't carry the bag on.
I'm not going to leave it there.

I always just assumed they would take it and it wouldn't make the flight...