Let me see how I get on = Let me see how it goes time wise = regarding time You can use (something) wise to say with respect to, regarding, in this way, etc. I'm OK to go on holiday money wise but I'm nut sure time wise. - With regard to money, it's OK, but with regard to time, I'm not sure. For the original sentence, you could say: Let me see if I have time, but I don't think I will.

I guess "time wise" here is equivalent to "with respect to time". So I guess the meaning would be "let me see if I can manage to be in time"

It means the person doesn’t think they will have enough time to do what the other person wants.