One of my Mom's caregivers wants to charge me "time and a half" for working New Year's Eve. (24 hour shift) Any advice?

Most Private Contractors these days want cash and take out their own taxes.
$10 to $15 an hour is not expensive. You are paying them to do what you don't want to so why should they work for minimum wage when jobs like the one you offer are plentiful and will pay far better.

Well it's a moot point now, since the holiday has passed, but for the future I actually don't think $10/hour is out of line. I'm just not sure that I agree with the under the table payment. Hope it all worked out ok.

Come to think of it, I don't think New Year's Eve is a holiday, anyway.
I'd prefer to take out taxes, but she wanted it this way.
She said she wanted $160 because she's awake 16 hours and won't get paid to sleep here. So, I thought, "ok, it makes sense to me." Of course, it includes food, too.
I'm not trying to be cheap. I just don't have a lot of money.

Is New Year's Eve a holiday?

Definitely take out taxes, it could come back to bite you and her both.

Most people get time and a half for holidays, so if you like her i;d do it. But not "payable to cash"...LOL

If I wanted her there and she is responsible for caring for my mother (mine is 95), yes, I would pay her time and a half. Can it all be spelled out in a contract, from now on?

Are you paying her "under the table" to avoid tax consequences?

I'd say an employee who works holidays should be paid extra. But I'd say arrangements should be above-board and legal, too, so I am not sure that my advice is what you are looking for.

Well, I can understand an employee wanting extra pay to work holidays as they are away from their own families.

$160 for 24 hour shift comes to $6.67 per hour. My boss was paying $15/hour for his non-agency Caregiver to care for his wife who had late stage Alzheimer's. His Caregiver wanted extra for the holidays, and he wouldn't pay... he went through quite a few Caregivers because of that, thus it was always a new learning curve for each new employee.