If you have relevant insurance which includes rental insurance, your rental should be paid for by your insurer, at least up to policy limits.The other party (the at-fault driver) would have to pay for rentals for a reasonable time IF you sue him or her and win, and the court decides (as it very well may) that part of your "damages" was the cost to rent and orders the other driver to pay. However, until and unless you sue and win, anything they offer is voluntary--they do not need to offer to pay all your costs; and you, in turn, could refuse their offer and opt instead to sue for all the money to which you believe you are entitled.