Attorney said that we could put Mom in a nursing home and have medical pay. Options?

TC1 - as Jeanne said, she is going to need to apply for Medicaid. Please read & re-read her advise as use it as your guide as to how to best approach the spend-down.
Now Medicaid is an "at-need" program, they must be able to show the "need" that is documentable. For NH Medicaid, they have to meet whatever your state has as it's limits for finances and then also they need to qualify medically. For medical, it must be that they need "skilled nursing services", so you want to make sure that mom's health care chart shows that. You may need to work with her doc to get this established too. I had to do this for my mom as she was coming from IL to a NH. Most NH admits are from a hospitalization to a rehab discharge to a NH, so those have the medical part soooooo much easier. For the financials, google your state Medicaid for NH to see what $ the limits are for her income and assets. It varies by state. Again, you really do want to spend-down as Jeanne suggested and then work back the money to get to the limits set by your state. Good luck.

If Dad was a wartime veteran, look into VA Aid & Attendance benefits for mom. She can get up to $1113/month from VA

Your conversation starts with her MD. The MD determines the level of care, the attorney only addresses the legality of it. MediCal will want five years of financial records, which have to be squeaky clean. That means all assets and expenses must be accounted for. Hint: they hate cash withdrawals and you need all receipts for expenses. They hate gifts of cars, homes and money.

Does the home she is in accept Medicaid payments? Some do after a certain length of self-pay.

But if Mother's dementia is getting worse, she may need more care than she is getting currently. In that case a nursing home might be a better option regardless of the finances.

One way or the other, it sounds like she is going to need Medicaid. One option for the remaining funds is not to use it all for the care home but to spend some of it on things Mother will need in the future. Once she is on Medicaid she will have a small personal allowance. It may be enough to get her hair done and send a few greeting cards but not much more. Therefore many people like to make sure the wardrobe is sufficient, they have extra pairs of shoes, perhaps get a deluxe wheelchair or a special chair, pay in advance for long magazine subscriptions, etc. That might mean she has fewer months left as self-pay in the care home, but is better equipped for the long haul. (The money must all be spent on herself -- she cannot give it to others or buy gifts.)

Discuss the "spend down" option with the attorney.