Several times I've encountered the idea that Lt. Col. Robert E. Lee, 2d U.S. Cavalry was offered the post of Federal Commander in Chief in early 1861. This is of course a nonsense. It seems to be based around Scott wanting Lee (who he knew from Mexico) for "a top command". Note it is not "the top command".
One thing that needs understanding is the nature of the U.S. Army List. Promotion upto the rank of Captain was entirely by seniority. Promotion to Major and beyond was more complex, but your ranking in the list was decided by the date of promotion to Major (i.e. entry into the Field Officer grades). Lee was an Engineer, a branch of service with extremely low promotion rates. Despite a Brevet Majority (some sources mention a Brevet Colonelcy, but this was never confirmed) he remained a Captain (seniority of 1838) until 1855, when he was assigned to be 2i/c of the newly formed 2d U.S. Cavalry. He remained in this post until 1861.
As war loomed Scott started to think about forming military departments. He initially selected 3 officers for the three departments; his choices were (in order of seniority) Fremont, McClellan and Lee.
Lee was moved to staff in Washington and was promoted Colonel of 1st U.S. Cavalry on 28th March 1861 (vice E.V. Sumner, promoted Brigadier-General*). He also provisionally accepted the offer of Major General of Regulars if Virginia didn't secede. After it was clear Virginia was seceding, Lee told Blair in person he could not accept a General Officer position on the 18th April, before resigning his Commission on the 20th. Shortly thereafter he accepted the Commission in the Provisional Army of the Confederate States of Brigadier-General offered over a month before.
Lee's putative Union command was given to McDowell. Thus if all other things had been equal then Lee would have commanded at 1st Bull Run.
* Congress offered 4 officers the rank of Brigadier-General of Regulars at this time; Sumner, Wool and Harney accepted, J.E. Johnston turned it down.