OOC: It's already been firmly established that the Confederacy won it's independence, and has been independent ever since, by Post 7 at the latest.
IC: Once again, the Union education/propaganda system strikes again. It is true that Grant's offensive at Petersburg in February 1865 severely battered Lee's Army. But in so doing, they suffered such horrendous casualties that the Army of the Potomac was pretty much gutted. They had to retreat to their own lines and were not an effective combat force for months afterward. Lee's Army was able to recover, and Richmond did not fall.
I am sorry to keep coming back to the military aspects, but some detail is important here.
Most historians, both from the US and CS surprisingly, seem to agree that if Lincoln had been re-elected the US would win the war simply through force of numbers, since they would have another 4 years to go at it. The CS historians, by and large, accept this argument, but just whitewash over it by praising Lee and the other leading southern Generals for prolonging the war long enough to get McClellan elected.
Newspapers from February 1865 are very lax on the details, so it is understandable to conclude that Grant just banged his head against Lee's defenses, as had happened for most of the past year. I only know the detailed story because I'm looking up stuff for a TL, where Grant's attack (not-so)-miraculously works, and McClellan is
forced to keep the war going because the US is so close to winning.
What really happened was that Grant and Lee were both planning great final offenses. Grant's was, as stated, a last-ditch effort to destroy Lee's army before the inauguration. Lee's effort was similar, to ensure the safety of his army until the inauguration. To do this, he had to avoid being flanked to the west. So being his traditionally devious self, he ignored his flank and planned an attack to the east of Petersburg, just north of Fort Haskell. Some of you may recognize the name - that was where the IXth corps assault took place (so this is for reference only, as the true location was nearer Fort Stedman to the north, but very few people know of the fort).
The man behind the plan was General Gordon, IInd corps commander. I need not go into details here - suffice it to say that it was by far the most complex yet most carefully designed assault plan in the entire war. If successful, it would isolate half of the Union army to the south of the breakthrough, causing Grant to contract his lines to contain it.
Grant's plan, meanwhile, was to have the IInd and Vth corps go on a flanking march, supporting by as much cavalry as the AotP and AotJ had between them, and roll up Lee's right flank, a good 20 miles to the west. He did not expect this to work, knowing Lee's calibre, but he expected Lee to withdraw troops from the rest of his line to reinforce the flank. At that point, simultaneously the IXth, VIth, and XXIVth corps would make a general assault along the line. There would have to be a break somewhere, through sheer force of numbers, and Lee would be crushed.
Lee scheduled his plan for dawn, Feb 18th. Grant struck on the 16th.
The 16th was a mess, the Vth corps got lost due to faulty maps, the IInd corps made some headway but hit Lee's strong entrenchments and was flanked on both side for a time (Mahone was the hero, of course), and the cavalry was occupied by Hampton's retaliatory raid. Nonetheless, it caused Lee to shift his only reserve, Pickett's division, from the left to the right of his line.
On the 17th the Union attack was more coordinated. Lee was, in fact, almost flanked, but the cavalry never moved far enough west. Pickett's men were in the right position, and halted the cavalry and one division of the Vth corps.
However, initial reports said only that Lee was weakening his line to reinforce the flank (which was not true - Pickett came from the reserve, not from the main line). Based on that, Grant made the general assault on the 17th, which hit Lee's strong entrenchments, captured some of the pickets, but basically was a bloody mess. The newspapers should have reported that, but for some reason they waited to put out the story.
Meanwhile Lee took a huge gamble, and during the night of the 17th weakened his lines everywhere to reinforce Gordon, who before dawn on the 18th made his own attack as planned. It worked and broke the IXth corps line, but could not be exploited. The IXth corps called upon every reserve it could find (and note that the all-black XXVth corps was accessible given a few hours with 10,000 men, but they were in a state of near-mutiny, as pointed out), and Parke just barely forced Gordon back. The US came off decidedly worse in the affair.
The newspaper stories just blended the 3-day battle into one thing and blamed Grant for all of it.
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Now, what would happen if Lincoln had been re-elected? This will make some changes militarily. Grant will have no incentive to make an all-out attack, and instead will continue to rely on out-stretching Lee.
Lee, on the other hand, has an added incentive to prevent Grant from doing this. As a last resort, he had been planning anyway to sacrifice Richmond to save his army, move south, join with forces there and stop Sherman's rampage (Lee took that march personally).
Observe: Pickett's division was originally slated to be Gordon's reserve. I see no reason why Gordon should not come up with the same beautiful plan as in OTL, but in TTL he will have at least 6,000 more men to do it with (possibly more, he also wanted a cavalry division).
So, some arbitrary date in the winter of 1865, Gordon attacks, breaks the IXth corps line, and throws Pickett's men in just as the Union is getting its reserves together. In OTL it took hours just to repair the break, in TTL I think the break will remain wide open.
If Gordon also had Hampton's cavalry, say, on hand, they can then charge through the break and keep on rolling up the Union line. Or, even better: the 10,000-men strike force keeps moving east. The City Point defenses had been built out of prudence. They were not hugely strong, and the garrison was a lot smaller than 10,000. If Gordon breaks that, and he only has like 2 miles to march to get there, he captures City Point.
I'd like to see even Lincoln continue the war if Grant, Meade, and the entire logistical train of the AotP and AotJ are POWs.