I am not aware of any law specifically addressing this, but I think several points can be made concerning the amount of time you have. First, if there is a lease and the rent is paid, then there may not be any basis to force a move unless the lease specifically addresses this situation. Even if the "lease" is simply month to month, the landlord should honor it. Next, it is wrongful to take any action to physically remove the belongings without going through formal court action even if there has been a breach of the lease. That would be true even if there is a provision in the lease that addresses this situation. A landlord must follow proper notice and court process to secure possession. Forcing the landlord to go that route would buy you more time than you have suggested, but it may result in court costs and attorney's fees being assessed against the estate. Next, if the rent can be paid, perhaps the knowledge that court action would be required, coupled with polite communication and payment in advance, could result in an agreement being reached for a reasonable period. Next, if the above zip code reflects your mother's place of residence, the City of Chicago has a very tenant favorable landlord-tenant ordinance. Other municipalities may have ordinances as well (check the city, village, county, etc.). You might look up the Chicago ordinance or you might find several organizations to which you can reach out if you search the web for Chicago Landlord-Tenant Ordinance.

First, check the lease. Depending on the kind of building it was, there may be a special form and special provisions. I have been involved in several situations where the landlord agreed to special termination provisions in case the tenant foresaw the possibility of decease prior to the end of the term, thinking this would help avoid a problem for the survivors. Given the short time period I would suggest immediately getting the lease into the hands of an attorney who handles both probate and landlord-tenant matters to evaluate.