Just pay the ticket. You could have received one for much more. You get no points for the failure to carry, and it's basically a favour that the cop did you.

I doubt they'll lower it at all, because $70 is like 2 tanks of gas, so if you can't afford this, you shouldn't be driving.

If they do somehow lower it, they won't drop it below half...so maybe to $35 instead of $70. However, that is doubtful, and to me, my time is worth a lot more than $35 for a half day at least. If you go to court you'll get a time of something like 1-4pm. Your case could be at 3:30, even if it only takes 5 minutes. Just pay the damn thing.