The battle with the largest number of killed in a single day was Antietam. James McPherson gives 6,300 to 6,500 as the death toll, which includes both those killed day of, and those who succumbed to their wounds over the next few days. He offers a few different estimates, but pegs roughly 2,000 Rebs and 2,300 Yanks as being a fair number for the day of casualties, and estimates that at least 2,000 would have quickly died of wounds, out of the 17,300 wounded (see page 177 of Crossroads of Freedom). He goes on to call this the single bloodiest day in American history. Other battles certainly saw losses much higher, even in the Civil War, but they were multi-day (like Gettysburg in the case of the ACW), or months long campaigns (such as Normandy during WWII).

So, I think that there really isn't much argument against Antietam, since even D-Day specifically didn't reach anywhere near that number in total casualties let along KIA, but of course, we are getting a wee bit of cheating due to the fact it was a battle where both sides were American! So what if we take those dastardly traitors at their word and don't call them American? Well, then we have 2,300 Americans killed, and, if distribution is equal and McPherson correct, ~1,000 who quickly died of wounds, for ~3,300 Americans killed that day.

• September 11 saw just under 3,000 killed (and not all American), so higher than the Union toll day of Antietam, but less than the +wounds number.

• Pearl Harbor saw 2,388 killed, which is just about equal to day of, and obviously lower than +wounds.

• D-Day casualties are only estimates, but total US casualties come to 6,774 according to here, but that is higher than the total deaths estimated for all Allied forces. Wiki points out "The original estimate for Allied casualties was 10,000 overall, of which 2,500 were killed. Research underway by the National D-Day Memorial has confirmed 4,414 deaths, of which 2,499 were American and 1,915 were from other nations." so main points being that I think we can place D-Day deaths as at least lower than the Union deaths when including died of wounds estimate.

• Attempts to find a breakdown of Gettysburg by day is a total failure, but Union (gotta keep it fair!) killed were 3,155 and 14,529 wounded. Using McPherson's ratio, lets say 1,680 of them soon died, for 4835 killed total. If deaths are even, that is a mediocre 1,612 per day or so, well under Antietam. To top Antietam, almost 70 percent of Gettysburg Casualties would need to be on a single day, which, given the hard fighting throughout the three day battle, is a very unreasonable assumption to make.

So anyways, that is the run down of other contenders. As you can see, taking McPherson's numbers, even if we just look at Union losses, it is hard to find another day which clearly gives Antietam a "run for its money". September 11th seems to come closest, and if we don't count those who succumbed to their wounds over the next few days, it is higher (although I don't know what number of 9/11 Victims were not American).