Can an employer deduct the gross amount for an overpayment?

1) They do need your consent (unless you signed any document or copy of an employee handbook stating that they may deduct in the event of overpayment, in which case signing same will be taken as furnishing your consent).
2) If you don't consent, they may take employment action against you (unless you have a written employment contract protecting you), such as demoting, suspending, or terminating you--that is because without an employment contract protecting your employment, you are an "employee at will" and may be terminated, or suffer anything less than termination (like suspension), at any time, for any reason. The could also, if they elect to, sue you for the monye.
3) You are wrong: they are entitled to the gross amount back because all of it was either paid to you (the money you received) or paid for you, on your behalf (such as your share of taxes). Payments made for  you convey a benefit on you. However, since are not entitled legally to any benefit from a mistake, you have to repay it all, You should be able to recapture or get back that money later: for example, if taxes were overpaid on your behalf, that overpayment will reduce what you owe in taxes at the end of the year or come back to you as a refund. While you have to keep records and follow-up, any overpayment on your behalf should come back to you, so you should not be losing anything by repaying the gross amount: only the timing of when you get the money (e.g. at tax time vs. now) changes.