Larger clients will often require you to have liability insurance. I was able to get some quotes for this as an independent consultant myself. However, given the extra expenses you'll have to charge more. I'd suggest using this higher cost as leverage toward the liability they want you to accept (for you, ideally as-is). I'd also explain since it's hourly if they dislike your work they can just replace you.

IANAL but my understanding is that for contractual work in the US you can only realistically be sued for at most the amount of the contract (supposing non-negligence). Asking you to accept liability beyond this sounds risky.