How do I tell my Mom that her generous giving habits have to stop or she will be broke soon?

Good answers! I agree with cwillie that your relationship is changing. You are now the parent, and she the child. You might humor her with writing out the checks but not mailing them. As a parent, you would protect your child, right? and not allow them to spend all of their savings, particularly if you knew that the future is uncertain. Maybe allow a token amount, say $10 to $25 in a check? and only for immediate family?

Let's stick the the truth.
A POA is not on the hook for the principle's care until Medicaid kicks in.
Medicaid does NOT go after the recipients of the applicant's gifts.

The truth is bad enough. If step mom runs out of money because she has been giving it away, there will be a penalty period before Medicaid would be available.

She might, of course, die soon, and none of this will matter. But that is not a given. And if it happens, any money left can be distributed via her will.

As P.O.A. take that cheque book home to 'make an accounting' for something so pick taxes, bank, whatever - THEN DON'T RETURN IT - keep forgetting it but write down who & what then say you'll take care of it -

Make a call to whoever it is & explain that if any money goes to them the federal medical aid people will go after THEM for money paid out - tell them you are trying to protect them so you get into the win/win situation with both but that mom was thinking of them - warn them not to raise issue with mom as you are writing out the cheque & if any money left over they get first dibs otherwise they get nothing

geewiz has the right answer! No amount of explanation, reasoning, arguing or showing is going to work with someone who has dementia. Five minutes (or even less!) later all that is gone. Poof. Like it never happened.
You don't explain in detail, but if all you are doing in bringing the check book and writing the checks in front of her, aka she has nothing to do with mailing them, the HUMOR her - write the checks and say you will mail them. Then just shred them later. The example geewiz talked about is still wasting money on cards, postage, etc. IF she is involved in mailing and you cannot get around that, then somehow either slip the checks out, void them or even better get a phony set of checks made up, not associated with an account (make sure everyone who might get one knows they are not real) and use them.
If her level of dementia is like my mother, simply writing them and promising to mail them is enough.

Thank you for your help The estimate was based on the cost of the assisted living and other bills. I have already told family to not accept money . I guess I will have to put up with her getting offended.

anereus, I like cwillie's idea of doing a budget. Just tell Step-Mom that every day items plus her rent are costing much more, so you both need to set up a budget so that she doesn't run out of money.

It's ok to use therapeutic fibs, saying if she runs out of money she would need to move to the "poor house", which your Mom may remember hearing from her youth. That in itself might be a major eye opener, or not.

Another fib you can use is tell her that Emily Post's Etiquette Book says that once a lady reaches a certain age that she is no longer required to mail gift money to family, a nice card or telephone call would be proper Etiquette. Thus, if your Step-Mom used Emily Post's books as a social guide [my Mom swore by those books], her ears will perk up at the name.

Your obligation as POA is to manage and protect her assets. This often conflicts with your obligation to your parent to reduce stress/anxiety. That said, if she continues spending/gifting like a drunken sailor, then YOU, as POA, are financially on the hook until Medicaid kicks in. Read very carefully Guestshopadmin's explanation.

She won't just be completely broke in a year and a half. She will be INELIGIBLE for Medicaid because she gifted away her money within the 5 year look back. And I promise you that none of the people that got gifts will be rushing to give them back.
Penalty works like this - stepmom gives away $50,000 during the 5 year look-back for Medicaid that could have been kept and used to pay for your care. Room costs $250 per day in nursing home (daily rates vary per state, this is for example purposes ONLY). Medicaid imposes a $50,000 penalty for gifting assets (it is NOT amortized so money given day 1 is treated same as day 1825). So she is not eligible for Medicaid for 200 days. Who is going to pay for the care in the nursing home during that period? The nursing home might have taken her Medicaid pending - and now the money that Medicaid would have paid is not coming. The Nursing Home looks to person with Power of Attorney to explain where the money to pay the bill is coming from .... and where the person is going to live if Medicaid is not going to pay the bills. Gets ugly very quickly. Don't tell her she is stupid - explain that you are protecting her money so that she gets care later if she needs it and doesn't depend on the government in case the programs get cut.

Can you bring a check book, let her write out the checks and (oh gee) fail to mail them? At one point the POA for MIL followed instructions to write out checks helped her address the envelopes, Mailed them and instructed everyone not to cash the check. I thought it would have been simpler to just not mail the holiday cards/checks but . . .

You have to wrap your head around the truth that your relationship with your mom is changing and you need to take the dominant role she once held. You can not sit back and allow her to destroy her future with irresponsible spending, it may be upsetting for you to have a frank budgetary discussion with her, but will it not be more upsetting to have cheques bounce or getting evicted from her home for lack of funds?