Leap days are caused by one revolution not being a whole number of rotations.
The weird thing with Mars would be that if you contact someone at 5pm local today it might not be okay to call them at the same time tomorrow, because they would clock in 37 minutes later.
Living on Mars in the next 100 years is already going to be hard enough emotionally, biochemically, and thermodynamically, without having a work schedule that changes by 37 minutes every day.
Everything about it, including the great distance, or perhaps especially the great distance says that Earthers will have to make the affordances. I expect anyone on Mars who didn't come through the ranks of the Armed Forces (and half of the ones who did), and any medical, psychological, or political scientist brought in as an advisor, are all going to give a big ol' "Fuck You" to anyone who suggests otherwise.
The weird thing with Mars would be that if you contact someone at 5pm local today it might not be okay to call them at the same time tomorrow, because they would clock in 37 minutes later.