I dont' know much about the intriccies of the Civil War, as far as what other genreals were what, but I recall the major ones, and I remember this was a very pyrrhic victory, if that, for the Union as it was; probably more like a bloody draw.
A bigger victory makes Grant more celebrated, and he probably advances the army further south after this. Lincoln later said of him, "I cannot spare that man; he fights." I don't think they can get as far as Vicksburg till late summer, but it will definitely embolden the U.S., to the point where the Emancipation Proclamation comes a few months early.
However, McClellan is going to be seen as the anti-Grant even more this time, as he loses the momentum he had going toward Richmond a couple months later. I foresee Lincoln dumping McLellan in favor of Grant in early July, letting someone else take over the Western army (Pope may be kept out West). That gives them the chance to have a Vicksburg siege by September or so, as the CSA focuses on the East more.
However, would they then send Jackson, who has proven himself to be very effective, to the West? I'm nto sure.
I'll leave that for the next one. Right nwo, I'll just say that Grant's aggressiveness will cause him to try andregain the advance against Lee's army. Now blunted, the invasion of Maryland is probably put off, and instead, there is a period sort of like the mid-1864 period of the ACW, only this being in July and August of 1862.
And, the Emancipation Proclamation is issued and takes effect the day the Constution was signed 75 years earlier, as a symbolic date.
Now, those who are much better versed can go into the intracacies and decide whether this even works.