As others have said, two donors can each fill out your reply device, put it in the mail prior to December 31st, and have it received after December 31st, except that one wrote a check and the other provided credit card information. The donor who wrote a check has made a gift in the previous year, but the donor who provided credit card information did not, because a credit card gift is only considered complete when the charge is processed against the donor's account ("Contributions charged on your bank credit card are deductible in the year you make the charge.").
This treatment (which is stated explicitly in IRS Publication 526, as quoted above and below) is an application of the general rule that a charitable contribution is made "at the time of its unconditional delivery." Once the donor writes a check and puts it in the mail, the check, which is considered the instrument of the gift, is considered to be outside the donor's control (which is why delivery by other means is treated differently). The application to the credit card gift is that the gift-the funds-have not been delivered to the donee until the charge is processed.
This is similar to the treatment of stock gifts, where gifts of paper certificates are considered complete when the certificate and the stock power have been mailed to the charity, but electronic DT transfers are not complete until the shares are in the charity's account. It has to do with when the actual gift has been delivered to the charity, rather than when instructions or authorization has been delivered to the charity.
(Historically, this treatment of credit card gifts is an improvement over the older treatment of credit card gifts, which was that the gift wasn't complete until the donor paid off the charge by making their credit card account payment.)
My US$0.02 worth; the usual disclaimers apply.
Good luck!
Alan
Alan S. Hejnal
Data Quality Manager
Smithsonian Institution - Office of Advancement
600 Maryland Ave SW Ste 600E
PO Box 37012, MRC 527
Washington, DC 20013-7012
Voice: 202-633-8754 | Email: HejnalA@si.edu