Torn CV boot
 

I guess when my control arm let go, it took the cv boot with it. The boot is still on, but it's definitely torn pretty good.

How long can I drive like this before it needs replacing/how dangerous is it?

I'm asking because my next day off is Tuesday, which is when I'm going to install a new axle. Until then, it's either drive it with a torn boot or don't drive at all. : /

You can quick boot it if you are worried about it, but I have heard many instances of people driving on torn boots for a long time. If you are going to put in new axle tuesday, assuming the cv joint didnt come apart, i wouldnt think twice about driving it until then. Just be wary of excessive speeds.

maybe put some duct tape around the boot to kep the grease in.

It's going to sling grease, but should be fine for a while. Once water gets in there it will start to wear and get sloppy.