I wrote something on this somewhat recently which I'll repost here (stitching in several follow-ups):

Winfield Scott, 'Old Fuss and Feathers', was the ranking general of the US military in the spring of 1861. He was also 75 years old, weighed 300 pounds, and was wracked by gout. He was no field commander. Robert E. Lee was considered one of the more brilliant officers in the army at that time. He was respected, capable, and experienced. He was recalled to Washington to take a commission to Colonel at Scott's insistence to Lincoln, but the recall was in actually for more than that, as Scott knew he couldn't lead this war, and knew only one man he wanted to take the reins.

On April 12, Fort Sumter was fired upon. On April 18th, Lee was to meet with Scott. Rumors were already in the air that Virginia was going to declare for the Confederacy, but they had not yet announced it, even though the process had begun by then. Prior to his meeting with Scott, he first met with Francis Preston Blair, an adviser to the President, who Lincoln had sent to sound Lee out and unofficially convey the offer that Scott was going to officially lay before him that morning: Elevation to two star rank, and effective command of the military effort against the Confederacy. Scott would remain in rank, but Lee would be his de facto designated successor to take over once he retired, and in the interim, direct the war in most practical terms.

Scott knew his limitations, and needed a deputy who would be capable of prosecuting the war in the field, and Lee had been far and away his first choice, and recommendation to Lincoln for the post. Scott's opinion truly knew no bounds, having declared that if one man were to lead the defense of the country, "I would say with my dying breath, let it be Robert E. Lee". Advising Lincoln of this, Lincoln agreed to the promotion and appointment.

Lee told Blair what his answer was, despite Blair's repeated attempts to convince him otherwise, but nevertheless Lee dutifully reported to Scott, where he reaffirmed his refusal to take up arms against the South and against his home state - a tad ironic of him to tell Scott, himself also a Virginian - "Lee, you have made the greatest mistake of your life, but I feared it would be so" he is reported to have said. To be sure, it was a tough decision for him by all accounts, and after telling Scott he could not lead a war that may require the conquest of Virginia, he continued to wrestle with it. The Confederacy had offered him a one star commission in March, when he only knew he was going to be a Union Colonel, but he had declined that as Virginia remained uncommitted at that time, not even sending a response. The initial vote against secession on April 4th seemed at first that it might even prevent him from having to be placed in that position, but by the middle of the month, in the wake of the call up for 75,000 volunteers on April 15th, Virginia was clearly sliding away. Even as late as April 14th, Lee had given muted, if positive, words for the Union, praising (Southern) Major Anderson's hopeless but honorable stand. Still though, at least until Virginia was officially out of the Union, he was not settled on resigning his command, and thus if it remained, he felt that it was his duty to accept, since, as he wrote to Scott two days later, he was hard pressed to "separate myself from a service to which I have devoted all the best years of my life and all the ability I possessed."

As it turned out, his internal - and external, as he consulted with his brother Smith later that day, himself caught in the struggle - debate was for nothing. The 19th saw the announcement that the Secession Convention had voted in secret two days earlier for secession. It would not be official until a referendum the next month, but any chance of Lee changing course was now passed by. Observing her husband upon hearing the news, Mary Lee called it "the severest struggle of his life". He wrote his resignation the next day, alongside a note of apology for Scott - "Be pleased to accept my most earnest wishes for the continuance of your happiness and prosperity, and believe me, most truly yours...". On Scott's part, he "mourned as for the loss of a son."

It is again somewhat ironic that this drama played out between two Virginians, one feeling that he was honor bout to his state, the other demonstrating an honorable path of Union, responding to fears that he might take the same path to note "I have not changed. I have not thought of changing. Always a Union man" - not that it prevented some Virginians from first trying to recruit him, and upon refusal lambasting him, especially compared to the 'noble Lee' - "[...] two names will be held up to the execration of mankind-that of Benedict Arnold and your own...".

With Lee gone, the next choice Scott considered was Albert Sidney Johnston, who commanded the Department of the Pacific, but he too was a Southern mad and resigned before any offer was even made. Running out of qualified options, Joseph K.F. Mansfield was suggested by Scott too. He commanded the Department of Washington, but had very little to make him stand out. In the end, a mere Major, Irvin McDowell would be the man on which command eventually fell. He was a decent staff officer with no field experience worth mentioning. Scott knew him well, as McDowell had been on his staff previously, but thought little of the choice, which was effectively forced upon him by Salmon P. Chase, the Secretary of the Treasury. The choice was a poor one for many reasons, angering many officers senior to him - for which he refused two stars and took only one - and of course, he was in command at Bull Run which should speak volumes.

IT isn't like there were that many solid alternatives though, of course, since the fact that Lee was chosen illustrates the slim pickings. It we evaluate the higher command of the US Army at the time, no Department head was suitable,. John E. Wool who commanded the Dept. of the East was even older than Scott. William S. Harney, who commanded the Dept. of the West, had prominent Confederate connections in his family, which not only made him unsuitable, but torpedoed his career despite not turning to the Grey. Johnston and Twiggs - heads of the Pacific and Texas Depts, respecitvely - went South of course. The upper grades of officer-ship had been gutted by defections. In fact, once Virginia seceded, and with it those Virginian officers inclined to do so, according to Sears, "not a single Union officer had led as much as a brigade, in war or in peace" aside from the aged Scott and Wool. There was simply a dearth of higher command experience.

As such, despite being only a Colonel, Lee was still one of the more experienced and capable officers in the whole Army, giving his nomination quite a strong case even in spite of Scott's personal affection. There was only 1,108 commissioned officers in 1860, 1 (Scott) a 2 star General and 3 of them holding a single star. Even the bureaus and departments were commanded mostly by Colonels, although several held a brevet rank of brigadier. Lee was by no means one of the senior Colonels - literally bottom of seniority if anything - but he was the kind of young, insightful leader Scott wanted for the army. And by young, I mean that although Lee 54, the average colonel was aged 63 and, as the official army history of the period wryly notes, "mostly old men set in their ways". Time to rank was simply massive, with an infantry officer, if they ever reached it at all, taking 37 years on average to reach Colonel.

So while at a glance it might seem strange to have plucked Lee up from Colonel to be the second in command for the whole military, Lee was not a nobody in Army circles. He was as much of an ascending star as was possible in the staid antebellum Army, where promotion was slower than molasses and retirement ages not a serious concept. The promotion and seniority system of the Army in that period was utterly broken not just by modern standards, but by a reasonable assessment in the context of the times, I would argue, and it is entirely reasonable, even, for Scott to be well aware that following any sense of seniority would be disastrous. We can only speculate, but had he accepted the appointment, even those senior to him would have had the good sense to gripe privately at most.

In any case, the entire transaction was essentially kept secret at the time, although rumors of course began to circulate, and by the end of the war the broad outline of the offer for command to Lee was known as a general fact, even if not in every particular. Lee wouldn't have been a quite household name, and certainly not in the way Scott knew him and regretted his loss. The earliest publication I can find which sketches out the basic narrative of his declining the offer, and even includes his letter to Scott and several personal ones as well was published by William Parker Snow in 1865 - "Southern Generals: Who They Are, and what They Have Done", and of course it is unlikely that such information was a particular bombshell at the time either.

During the war, Lincoln doesn't seem to have commented with anything particularly noteworthy, although others noted that he was 'anxious to give Lee command' having trusted Scott's recommendation. For the professional soldiers, at least, some still held respect for Lee, and Irwin McDowell, at least, when making his HQ on the grounds of Arlington house, refused to make use of the house which he considered Lee's still, and was not going to enter it and take it over during the early point of his time there, and generally tried to avoid entering even after it was officially confiscated. But how widespread the awareness might have been is slim.