Well, it doesn't work that way. You should know that gov't rules don't apply to itself! Seriously, I haven't read the actual statutes, but I suppose how this is accomplished is that the authorizing legislation for the credit card payments has an override clause for any conflicting rules.

In any event, the way it works is that the US federal government doesn't directly take credit cards - you have to use an authorized third-party payment company. I know of at least two. The third-party company charges your credit card for the taxes (in two transactions - one for the tax due, and one for the "convenience fee"). Then, they foward the tax payment to the government. So, the government receives a check or similar instrument from the payment company very much like you had sent in a check yourself. Any extra money you pay has to be refunded directly from the government in the normal way.

So, theoretically you could take advantage of this to get extra miles. As cactuspete already pointed out, you have to pay 2.5% of the total payment, including the overpayment, made to the credit card. Plus, you don't get your overpayment back until after you file your tax return.

So, you could make a credit card payment with your Form 4868 filing (automatic extension to file) on April 15, then on April 16 file your actual return electronically, and request that your refund be ACH'd to your checking account. In ordinary situations, you'd have your refund within 14 days of filing. However, it's likely that they won't process your refund until they have all of your payments for the year posted (which would include W-2 withholding, 1040ES payments, and most importantly in this example, the 4868 payment). I doubt that this happens instantly, so you may end up waiting a few more weeks. Interestingly, unlike your tax return itself, even the paper 4868 does not require your signature, nor are you making any declaration that the information is "true, correct, and complete," so it would seem that there is no potential criminal penalty for doing this scheme. (In the case of an underpayment, of course you're still liable for late fees and interest, and potentially criminal penalties, but this is because of the underlying problem of not paying your tax on time, not because of anything done on the 4868).

Please note that I'm not an attorney, and I give no warranty to any of the above.

Woodsmit, you're not the first one to have thought of this!