How likely is it that a deferment can be approved if they are 3 weeks from deploying and I was granted orders under MACP?

When units ramp up for deployment there are systems that are put in place to designate and train the people going. If you weren't already designated, you won't be eligible to go even if you deferred your orders.
The second issue is getting a deferment in the next three weeks isn't going to happen. That's a request processed through S1 to HRC and signed by the Brigade commander. That's just not happening in three weeks.

Contingency deployments, have a higher priority. MACP, unfortunately, is not guaranteed to you 100%. If your Commander has decided to place an stop move on you, your PCS orders will be deferred to 90 days after the date of return from deployment. Talk to your chain of command first to see what their plans are. If you reenlisted for this assignment and it is on your contract, Your battalion Career Counselor needs to know what is going on with you, so he/she can take proper actions.