Posted this elsewhere and the response I got made me do further research.
Of note is the OR of Rosecrans:
We had lost heavily in killed and wounded, and a considerable number in stragglers and prisoners; also twenty-eight pieces of artillery, the horses having been slain, and our troops being unable to with draw them by hand over the rough ground; but the enemy had been thoroughly handled and badly damaged at all points, having had no success where we had open ground and our troops were properly posted: none which did not depend on the original crushing in of our right and the superior masses which were in consequence brought to bear upon the narrow front of Sheridan's and Negley's divisions, and a part of Palmer's, coupled with the scarcity of ammunition, caused by the circuitous road which the train had taken, and the inconvenience of getting it from a remote distance through the cedars. Orders were given for the issue of all the spare ammunition, and we found that we had enough for another battle, the only question being where that battle was to be fought.
“Personal Recollections of the Battle in the Rear at Stone’s River, Tennessee” in Sketches of War History 1861-1865: Papers Prepared for the Commandery of the State of Ohio, Military Order of the Loyal Legion of the United States., Volume VI -
As aide to General McCook, assigned to duty as ordnance officer of the right wing, I had charge of some seventy six or seventy seven heavily laden ammunition wagons, as I remember, each drawn by four horses or mules. General McCook had the largest corps in the army, and his ammunition trains were relatively large. But a single infantry company of about seventy five men and two mounted orderlies had been assigned to me as train guards. I was proud of this new command, but these ordnance treasures carried with them grave responsibilities…Danger already threatened, and it was soon prepared for movement…I decided to direct my train toward the center of the infantry line, keeping well to the front. At the very start a detachment of Confederate cavalry charged wildly upon the train, attacking and endeavoring to stampede our teamsters and animals, but with the aid of the plucky train guards and some help from Captain Pease, of General Davis’ staff, we repulsed the attack and moved on…
While in the open ground, moving our ammunition train rapidly to the left, it was discovered by the enemy. In my anxiety for its safety, I had already reported the importance of the train to every cavalry officer within reach, and appealed for protection. Colonel Zahm, of the Second Ohio Cavalry…promised me all possible help, and promptly formed his regiment in line for that purpose. Major Pugh, of the Fourth Ohio Cavalry, at my request also placed his regiment on our flank, facing the enemy. The First Ohio, Second East Tennessee, and a battalion of the Third Ohio Cavalry were near at hand.
Alas, when the crisis came, a few minutes later, they were not in position to successfully withstand the shock. They were unprepared, and not in brigade line. Wharton’s Confederates unexpectedly appeared in great force. His artillery opened fire furiously upon the Fourth Ohio Cavalry, and threw the regiment into some confusion…
Soon apparently his entire command charged down upon us like a tempest, his troopers yelling like a lot of devils. They first struck the Fourth Ohio, which could make but little resistance. Colonel Minor Millikin, the gallant commander of the First Ohio, led a portion of his regiment in a most brilliant counter charge, but it had to retire with fearful losses. In the onslaught the dear, fearless colonel, my intimate college friend, engaged in single combat with a Texas ranger, and was slain.
There was no staying the Confederates. They outnumbered and outflanked us, and to tell the melancholy truth, our defending cavalry retired in confusion to the rear and left the ammunition train to its fate–high and dry in a cornfield. As may be imagined, our teamsters, the train guards and the ordnance officer (yes, I must admit it) were not left far behind in the general stampede. We fired one volley from behind the protection of our wagons, and then hunted cover in rear of a friendly fence and in the nearest thicket…The Confederates began to collect and lead away our teams and wagons, and our condition seemed desperate–indeed, hopeless.
Happily this appalling state of affairs did not last long. Some of our cavalry rallied, other Union detachments came to the rescue. Wharton had soon to look to his own flanks, and was kept too busy to carry off our train. The conflict fortunately shifted. Captain Elmer Otis, with six companies of the Fourth Regular Cavalry [4th U.S. Cavalry] , attacked Wharton’s command with great vigor and success. Soon two battalions of the Third Ohio Cavalry came up from the rear…and nearly every wagon was finally recovered…and we were soon moving toward the Murfreesboro pike and the left of our army at double quick speed.
The enemy, still bent on destroying our train, followed us like sleuth hounds. Pat Cleburne’s artillery fired some hot shots at us from a hill on the main battlefield, and just as we reached the Murfreesboro pike General Wheeler’s troopers charged furiously upon escort and train and captured several wagons, but with the aid of our infantry they were soon repulsed, and the wagons recaptured.
Thus ended for the day the campaign of the ammunition train. Our army front on the new right, was finally established, and for the first time in many hours train guards and animals breathed freely and rested in safety.
In essence, if Wheeler had supported Wharton, as McDonough proposes as a missed opportunity, not only is the Nashville Pike cut
but McCook's 18,000 men are out of ammunition by 12 PM on the 31st. Rosecrans would only have 25,400 equipped men to Bragg's 35,000 and basically his entire right flank would collapse.