This conversation took place (assuming it is relayed accurately) in the dark days of August 1864, when Grant's assault on Lee's army was stalled with appalling slaughter, Sherman had not yet taken Atlanta, and a wave of war weariness was overcoming the electorate. Lincoln's honest parsing of personal ambition and love of country at the outset is itself remarkable, if characteristic, but his read on the military/political/economic forces at work is even more remarkable -- at least to this moderately informed reader. The source below is Hay's short version of the ten-volume biography he wrote with Nicolay. I don't know whether the ellipses appear in the full biography.
Mr. Lincoln realized to the full the tremendous issues of the campaign. Asked in August by a friend who noted his worn looks, if he could not go away for a fortnight's rest, he replied: "I cannot fly from my thoughts—my solicitude for this great country follows me wherever I go. I do not think it is personal vanity or ambition, though I am not free from these infirmities, but I cannot but feel that the weal or woe of this great nation will be decided in November. There is no program offered by any wing of the Democratic party, but that must result in the permanent destruction of the Union."Asking myself again what's new to me in this: I knew that Lincoln justified emancipation as a military necessity. I knew, too, that the southern slave workforce largely evaporated in its wake. I knew that African Americans' manpower as soldiers and nonmilitary servants of the army was important to the North's war effort. I did not know that in Lincoln's view the North lacked the power to successfully prosecute the war without that aid -- that in fact after three years of slaughter African American manpower was in his view as vital as air or blood to the Union effort.
"But, Mr. President," his friend objected, "General McClellan is in favor of crushing out this rebellion by force. He will be the Chicago candidate." "Sir, the slightest knowledge of arithmetic will prove to any man that the rebel armies cannot be destroyed by Democratic strategy. It would sacrifice all the white men of the North to do it. There are now in the service of the United States nearly one hundred and fifty thousand able-bodied colored men, most of them under arms, defending and acquiring Union territory. The Democratic strategy demands that these forces be disbanded, and that the masters be conciliated by restoring them to slavery.... You cannot conciliate the South if you guarantee to them ultimate success; and the experience of the present war proves their successes inevitable if you fling the compulsory labor of millions of black men into their side of the scale.... Abandon all the posts now garrisoned by black men, take one hundred and fifty thousand men from our side and put them in the battle-field or corn-field against us, and we would be compelled to abandon the war in three weeks.... My enemies pretend I am now carrying on this war for the sole purpose of abolition. So long as I am President it shall be carried on for the sole purpose of restoring the Union. But no human power can subdue this rebellion without the use of the emancipation policy and every other policy calculated to weaken the moral and physical forces of the rebellion.... Let my enemies prove to the country that the destruction of slavery is not necessary to a restoration of the Union. I will abide the issue."
Nicolay, John George (2012-05-17). A Short Life of Abraham Lincoln Condensed from Nicolay & Hay's Abraham Lincoln: A History (Kindle Locations 5668-5683). . Kindle Edition.
There was always a certain cold-bloodedness in Lincoln's stated case for emancipation. As he famously wrote to Horace Greeley in 1862, "My paramount object in this struggle is to save the Union, and is not either to save or to destroy slavery. If I could save the Union without freeing any slave I would do it, and if I could save it by freeing all the slaves I would do it; and if I could save it by freeing some and leaving others alone I would also do that." That sentiment is extended in the dialogue reported above. There's a measure of political self-protection in it, as when politicians today argue that policies that benefit the poor will stimulate the economy. But standing behind the utilitarian argument -- we can't save the Union without emancipation -- is the moral imperative that Lincoln started with -- that the Union (and democracy) could not survive without at least stopping slavery's expansion -- and the further development in him of that moral imperative, to the point where in 1864 he stated that he (and the union) could not betray the emancipated slaves who had shed their blood for the Union, and in 1865 wondered, in his second inaugural address, whether God's will was not behind the logic of war that destroyed slavery while perhaps also ensuring that "every drop of blood draw with the lash, shall be paid by another drawn with the sword."