can i draw up a will 2 days before persons death

A challenge to a will may be brought by anyone with an interest in it who believes the document is invalid in some way.  A "will contest" is an action challenging the validity of the will.

If you believe a will is invalid you should contact an attorney with experience in will contest cases. They can assist you with this type of difficult and emotionally-charged case, and can advise you on the best way to proceed under your state's laws.

Grounds for contesting a will include:

Later Will.  If a later will was made, and the making of the will conformed to the necessary legal requirements, then the later will replaces the earlier will.

Incapacity.  A valid will requires that the decedent was of sound mind at the time the will was made. The "sound mind" requirement typically requires that at the time the will was made, the decedent had the ability to generally understand the nature and extent of the property to be disposed, his or her relationship to those who would naturally claim a benefit from the will, and the practical effect of the will as executed.  Proving that the decedent was mentally ill or under the influence of alcohol or drugs at the time the will was made are ways to establish incapacity. 

Undue Influence.  If at the time the will was made, the decedent did not exercise his or her judgment in making the will, but rather made the will according to the wishes of another, the will may be found invalid on the grounds of undue influence.  Coercion, duress and fraud are examples of undue influence.

Improper Execution.  A will must be properly executed in order to be valid.  This requires that the creation and the execution of the will conform to the state's requirements, which can include the will having to be in writing and signed by the person making the will (the testator) and that the will be witnessed.

Forgery.  A will can be found invalid if any portion of the will, including any terms of the will or the signature of the testator or the witnesses, are determined to be forged.

There is a limited amount of time set by state statute to challenge the validity of the will on one of these grounds.  If the validity of a will is successfully contested, the probate court may: disallow only that part of the will that is successfully challenged; admit an earlier valid will (if one was made) in its place; determine that the decedent died intestate and distribute the assets according to the state's intestate succession laws (which are the legal default rules for estates without a will).

As to your specific situation, since the will was executed so close to your grandmother's passing there might be potential challenges to it on the grounds of incapacity and/or incompetence; of course you will need proof of this.  Absent a showing of grounds, a will cannot be contested just because it was executed so close to the decedent's passing; technically a will can be signed right up until the time of death.   Additionally there is no requirement under state law that a will be notarized (although it is recommended); and only 2 witnesses are required.