They cut off phone check-in feature something like at least an one hour before the flight so by the time you realize you will be late it is too late to use the phone.
Checking in by phone ahead of time can be worse. I have never been able to use the ITM to print my BP after phone check-in, like you are suppose to. So when you check-in by phone you WILL have to wait in line for your BP and you know even the FC/MVP Elite line can be really slow at times as the only people standing in line have lots of luggage. But if you skip phone check-in and make it, let's say, 35 minutes prior, you can check-in and go straight to your gate without having to wait in line.