In most states, certain food items are taxable. For example, in NY, sales tax is charged on soda, wine and beer. If this is included in the sale of my chametz, and I don't charge the buyer tax, I may be breaking the law. Would that invalidate the sale?
Per here as long as you sell the item from your home, and don't deliver it (and several other limitations) you do not have to pay sales tax. If you happen to sell more than $600 worth, but didn't intend to, then you have to pay taxes on the rest. But that is only true after the fact, so you don't have to register.
So the upshot is that since you don't expect to owe sales tax on more than $600, the general case of the individual selling Chametz is not a problem.
Businesses, however, may face other complications, as they don't fall under the same exemption.
By the way, you are under no obligation to charge the buyer the tax. You (the seller) just have to pay it.
It would seem to me that in the state on NJ this would be considered a "casual sale" and would not be subject to tax.
Under :Seasonal, Occasional, and Casual Sales
Sales by persons making isolated or occasional sales of items of tangible personal property which were purchased by them for their own use are considered to be “casual sales” and are not subject to tax. Examples of casual sales are one-time sales of household items, children’s toys, tools, etc. at a yard sale, garage sale, or through a classified ad.
Other answerers have disputed your premise that you'd need, under the law, to worry about sales tax. I'll grant arguendo that there's a sales-tax issue but dispute another premise: that you need to charge your gentile customer the sales tax. Stores frequently have "we'll pay the tax!" sales. That is, instead of charging you $108 for a $100 item and forwarding $8 (for example) to the government, they charge you $100 only; they then forward $7.41 to the government, because 8% tax on $100−$7.41=$92.59 is $7.41. But it's not only for special sales that stores do this: every time they make a sale, they later forward about 7.41% of the money to the government. And they do it every so often, not after every sale. You're effectively doing the same with the non-Jew: you are selling him chametz and later will forward about 7.41% of the sale price to the government. If you wind up not doing so, that's an issue later between you and the government, and has nothing to do with the validity of the sale. (No source for that last half-sentence of my answer, but it seems obvious to me.)
 Again, that's assuming you need to.
I double checked with my LOR and besides the laws of New Jersey and New York shown in the other answers, the normal behavior throughout the country is that private one time sales are not charged sales tax. That is, when you see an ad in the paper for someone selling an item, the buyer is not charged sales tax and the seller (not being a business) does not have to fill out the sales tax forms and send the money to the government. Each state has its own specific laws (as we see in the other answers) but the general rule in the United States is that sales tax does not apply to this kind of sale.
Note that my LOR is not saying this as a lawyer, but as someone who is familiar with the practice of how rabbis in the United States sell chametz to nonJews for Pesach and buy them back afterwards. If the government changed the laws to force people to pay sales tax on the individual items that they sell via classified ads or yard sales, then the problems would encompass many more people. In any case, the payment or nonpayment of a tax to the government for private sales of this type would not invalidate the sale (halachically), which is the point of the original question.