We must remember that a lot of what Meade was considering was personal apprehension in his remaining command structure and probably NOT relayed to Lincoln by any message.
What Lincoln would have recieved would have been by Telegraph, which would have been short messages, which would give Lincoln little real insight into the Union Army's actual condition. On top of this you would have had a time factor on those messages.
Lincoln was not a trained military commander. He and Meade would have looked on the matter with differing viewpoints. Lincoln in his comments about replacing Burnside with Hooker earlier that year had commented that he wished he could find a General that understood the "Horrible Math" of this war, that even with the union casualities of such battles as Fredericksburg, the Union army could sustain those casualities of 10 such battle and destroy the entire ANV Army if he could find a commander who would press the Confederates and continue to inflict the same level of casualities on the Confederates that Lee suffered at Fredericksburg.
Well NO army Commander thinks that way in normal military circles. This is what made Grant so effective in 1864 was that he did understand Lincoln "Horrible Math". And also why he was called "Grant the Butcher". And because of his "Horrible Math" comment, which reflected his attitude, Lincoln must also share in this title. No Commander is every willing to lose all of his men no matter what the objective even to end a war. Career Officers are not trained to think of an army in those terms. They are trained to look for an advantage, to flank, or out manuver the enemy so as to defeat him with the least loss of their own army. They are willing to lose a portion of their command to obtain a specific objective, but never all of their command. They always will want to save a portion of their army to fight another day.
Now Lincoln on the other hand, being the politician, saw only one objective, and one consideration, the total destruction of Lee's Army at any cost to end the war.
Meade's decision not to press Lee's retreat, which on its face would have been a reasonable military move, evidently was based on the physical condition of his Army and his evaluation of those intangible factors that are the indefinable part of any decision making process. Lets remember the famous Council of war that Meade held on the night of July 1st/2nd in which he relied upon the judgement of his field commander to make the decision whether to stay at Gettysburg or withdraw. He did this because he was not familuar with the Battlefield, or the condition of his army, at that point. With the loss of even more of his key commanders by July 3rd, surely he would have been even more concerned about the army's condition and whose advise he could rely upon. I am sure that Meade would NOT have been able to relay this type of detailed information to Lincoln in anything other than a full report delivered personally. This is possible why we have no record.
I make this observation based on the fact that Meade was one of the more aggressive Corp commander in the Union army and wished to press the attack at Chancellorsville rather than withdarw as Hooker ordered, and would have, under normal circumstances, taken advantage of an oppertunity. Because it is so out of charactor is why we question why Meade didn't follow after Lee and make the false assumption, as Lincoln did, that he failed in his duty, or was in some way possible a coward, for not doing so.