I don't understand what you think contacting the landlord would do?
If the part won't be here until Tuesday the landlord will not be able to get it any quicker.
This is not just a rental thing, when we owned our house and the heating broke down we were without hot water and heating for a week whilst they sourced the bit.
They can book into a hotel and try and claim the money back from either their insurance or the agents but I guess they would have had to have had permission before going to the hotel.