What does it mean to wax a cross?

Solution 1:

It is not a common expression, but you have the basic meaning right.

Cross is a metaphor for the Christian cross, as in the expression have a cross to bear (ODO)

Have a difficult problem or responsibility one has to deal with

As a smoker, I can tell you it’s a horrible habit, but that’s my cross to bear.

But in the show, it is used sarcastically, to belittle a duty or someone pointing out a task or responsibility they must carry out. For example, in the episode Legs, there is a flashback scene where a doctor has directed the butler, Woodhouse, to call an ambulance for a seriously injured juvenile Sterling Archer. Ignoring the child, His mother, Malory, and the doctor begin flirting and make plans to attend an event downtown together.

MALORY: Oh! Well then I'll just get my coat.
WOODHOUSE: And I'll wait here? For the ambulance to take your grievously wounded child to the hospital for emergency surgery?
MALORY: Yes, Woodhouse, and then you can go buy some wax for your cross.

Woodhouse is incredulous that the mother is neglecting the boy, but Malory reacts as if he is complaining about having to wait, as if it is some great burden, some great cross.

To wax something, ordinarily, is to apply wax to it, usually for protection: skis, cars, floors, furniture (waxing your legs is a different sort of maintenance, one that actually strips away protection, but not the sense indicated here). One would need to buy wax regularly for anything that takes it, and a cross like Jesus', being wooden, could use a coating if regularly borne.

So when Malory groans "go buy some wax for your cross," she is saying Woodhouse is complaining inappropriately about a burden, and does so often. Therein lies the humor in this line, and a reinforcement of Malory as a haughty, unaffectionate, and unmotherly character, for Woodhouse is comically servile, dutiful, and taciturn around his ungrateful employers.