The query is confusing. In a short answer, a verbal contract is binding if it represents a meeting of the minds and depending on the amount and terms. In most states, over a certain amount the "statute of frauds" applies, meaning that such contracts are not enforceable unless in writing. There are other terms that bring the statute of frauds into play. Here, it is unclear what you refer to as your "verbal response." If you agreed to pay for advertising orally and you later cancelled the order, the advertiser may well have a claim for "quantum meruit" meaning the value of its services up to the time of cancellation. You should determine what, if any, services they provided in reliance on your order before the cancellation before paying them. Good luck!
I agree with my colleague both that the other party may have an equitable claim based on work completed and that a verbal contract can form a binding contract, but that it could be subject to the statute of frauds (meaning that a "writing" is required and that you must "sign" it to be bound by it). Whether the statute of frauds would apply depends on some more specifics (such as whether or not the "contract" contemplated that it would be completed within a year). An e-mail can in some circumstances satisfy the writing requirement of the statute of frauds. Whether or not they have a leg to stand on depends on more specifics.
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