I recommend contacting an attorney licensed to practice in Nevada with experience handling real estate litigation for advice on this matter, because the property is located in Nevada. In New York, there are remedies for deceptive consumer practices as well as wrongful conduct in the marketing and sales of real estate securities (condominiums, cooperatives, timeshares, etc.). That's not to say that those legal theories fit the facts here or that similar remedies exist under Nevada law. You should calculate your worst-case scenario in terms of how much you might ultimately end up paying for the timeshare and compare it to what you might spend on legal fees before diving into a lawsuit. I recommend asking any attorney you retain for a budget that will make this cost-effective for you.
Remember, your goal here should be to cut your losses to the extent possible. You're going to end up out of pocket unless you manage to recover attorney's fees. I recommend trying to decide how much you're willing to spend to fight this before you spend anything on legal fees, and compare it to how much you'll lose by keeping the timeshare (including, in the event of a default on the various fees, the damage to your credit score that would come from a foreclosure of the timeshare). Your best-case scenario is that a letter or two on an attorney's letterhead on your behalf will get you out of this, so I hope that's what happens here for your sake. Best of luck in reaching a favorable resolution.