You and your husband will receive the home as long as your grandmother left it to you in her will, or has titled the house in such a way that it will pass to you without probate. Medicare or supplemental insurance will only pay up to 100 days in a nursing home if she is in the hospital for at least 3 days and is discharged to the nursing home for rehabilitation. After that, either she has to pay privately or needs to qualify for Medicaid. She can't have more than $1500 to $2000 in assets (depending upon the state) in order to obtain benefits. As a result, the house may have to be sold to reduce her assets to the appropriate level.
As an alternative, check the Medicaid rules in your state to see what may be available to protect part or all of the value of the house. For example, if her money is gone, but the house hasn't been sold yet, she may be able to quality for Medicaid for a period of time even while she owns the house. In Ohio, that time is 13 months. After the protected time period, the house would have to be sold. However, at that time, you may be able to purchase the house at a discount or at least undertake some Medicaid planning in order to protect some portion of the sale proceeds.
Also, you may be entitled to keep the house as a caregiver who cared for her for a period of time. In Ohio, a caregiver child who moves in to the Medicaid recipient's home and cares for them for at least two full years prior to them entering the nursing home when they SHOULD have been in, is entitled to have the house transferred to them free and clear. Although the regulations in Ohio do not provide for a grandchild caregiver, your state may.
You may wish to contact an Elder Law attorney for more specific advice. Good Luck!