They claim the odor to smell like urine and although it's unpleasant, it isn't an emergency to me so do I stand my ground and not get back to them until Monday?

Once for cat urine.

Urine and feces soaked carpet , used needles , rotten food .  

Just consider what it would cost to replace the cabinets that they urinated in, the floors and carpet they urinated on, and paying the cleaning guy to clean the vents they urinated in (hopefully they didn't rust do the the glorious urine left in them). 

Why , rat droppings and cat urine are unsanitary . have all the windows and spray it down , be carefull you need good ventilation , dont spray on electrical outlets , it is a corrosive .  

So we inherited a tenant who has lived in the same unit for over 30 years and the place smells like feces, urine, among other things.  

Tenant, put coke's bottle in my mail box, I guess it has his urine in it.I called the cops and reported the incident.

For example, when our maintenance guys recently discovered dog urine on a tenant's carpet, we issued a $25 lease violation and required them to clean it up.That said I don't know the laws in Virginia and your lease may or may not allow for such measures.

Ever try to get urine out of grout?

Pictures are shown below but the one thing that is missing from the photos is the putrid smell of cat urine and feces (along with other odors too).