Is there a time limit after a person dies that the executor must execute the will?

There is no time limit, but your question troubles me. Who has the will, if not family members? No one is "executor" (the proper term in Oregon is "personal representative") until they are appointed as such by the probate court the designation in the Will is the decedent's preference, and is given deference by the court, but no one is "executor" until they have letters testamentary which are issued only by the probate court. If you believe that you are included in your mother-in-law's will, see an attorney about being named personal representative yourself. If nothing else, this will bring the person named in the will forward and force matters to issue.

MCL 700.2516 provides that a person having possession of the will of a deceased person is required to file it with the court having jurisdiction, generally the probate court in the county of residence of the decedent. The appropriate time is described as "with reasonable promptness after the death" of the decedent. It goes on to provide that "a person who neglects to perform this duty without reasonable cause is liable for damages that are sustained by the neglect". If a person willfully refuses or fails to deliver the will or codicil after being ordered by the court, that person can be held in contempt of court and subjected to penalty. Obviously, this applies only if there is a will. Not everyone makes a will but if they have not, any immediate member of the family of the decedent make seek to initiate administration of the estate. There are statutory priorities as to who has priority to be appointed but a petition to administer the estate when granted, leads to the appointment of a responsible party (the Personal Representative) who is charged with identifying assets, filing an inventory and after paying bills owed by the decedent and administering the assets, makes distribution of the assets to those persons pursuant to the terms of a will or under the Michigan statute if no will was made and admitted to probate. Even a creditor could petition for administration if no family member did so within 42 days after the death. If the will did not make provision for the wife or, in her opinion inadequate provision, the wife has the right to elect against the terms of the will and claim a share as allowed by statute.

There's usually not a good reason for delay. In Texas, a Will can be admitted to probate within 4 years. Even after that, under the right circumstances, a Will could still be admitted to probate. Fortunately, Texas law provides for exactly your situation. I strongly encourage you to visit with a probate attorney near you to learn about an interested person's rights to demand production of the Will.

It all depends on the state.

ORS 112.810(6) provides that the custodian of a will must deliver the will to a court having jurisdiction over the estate of the decent or to the personal representative named in the will within 30 days after receiving information that the testator (person whose will it is) is dead. There is no formal requirement I am aware of for when the named personal representative has to file the will. ORS 112.830 does allow the court to order a person to deliver the will to the court. If a decedent dies with insufficient assets to have to file a probate, it is common to not file for a probate.

California law specifies that a will must be lodged with the court within thirty days. Lodging a Will with the court is merely turning the original over to the court. If the estate is requires probate, you can file the petition anytime.