Yes indeed, if he has a contract he needs to pay or try to reason with them or beg for mercy as I said in an earlier post.
I only referred to a bolt cutter (and a few strong men to make it more effective) because I believe the following might happen:
OP signed up for storage with monthly payment (I assume that because it's usually how these things work). He tried to get out, but they insist on the contract. Now if he just bites the grass and realizes he needs to pay (month by month), he still wants to move his things out ASAP. Correct me if I am wrong.
And thats exactly where I believe they won't let him, they will insist on full payment up front or change the locks. HK storage facility style.
Of course their fear of him skipping town may be for a reason, but if they just decide to defacto seize his things without repossession order, then I think its just fair for the OP to break a $100 lock which he pays for anyway (they usually sell locks at those places). They already threatened him with throwing away ("clear out the stuffs") his things today (with deadline) if he doesn't pay his full amount, despite the fact that they hold on to 3 month deposit.