During the first part of the Civil War, the Union had top commanders that did not aggressively engage the Southern armies. Lincoln was very disappointed in their performance and dismissed several commanders including McClellan.
As Commander-In-Chief, couldn't Lincoln have issued an order to McClellan such as "You will engage the enemy immediately and not disengage so long as you have either a single bullet to shoot or a single soldier to shoot it".
Was it within Lincoln's constitutional power to give such a direct order to a field commander? Did Lincoln not give such orders because it would be "unseemly" or "insulting" to do so? Did Lincoln not give such orders because he didn't want to have to take the blame for any resulting failure? Or did he actually give those orders and the commanders refused to obey them?
If Lincoln did give such an order and the commander refused to obey it - would the refusal be insubordination, or was it within the discretion of a commander to refuse an order that he felt was ill-advised?
COULD Lincoln have given an order like you mentioned? Yes, but it would have been borderline insane and the people around him would have said so. Communication in the 1860s was slow compared to modern technology, obviously, and would have made such a preemptive order ludicrous. For example, if Lincoln had a telegram in his hands on a Monday night saying that McClellan or someone else had a certain number of troops, and the enemy was nearby, in theory he could telegraph something back like, "attack at dawn and don't stop until you obtain your objective." But what if the situation changed in the morning, and the enemy moved, or had started attacking from a different position, or a different army moved on Washington City, necessitating a redeployment by McClellan (or whoever)?
If telegraph wires were cut, or if the battle was especially hot and it was difficult to get messages to the commanding general (if he could even be found or reached), an immovable order like, "attack and keep attacking no matter what" could be disastrous. Counterattacks were a real thing, and if an offensive didn't carry its objective, whole divisions or brigades could be eliminated that might otherwise have been saved following a retreat and regroup. Although Lincoln and his cabinet were hardly shy about prompting action or giving directions about how an army should be used, once it was in the field and engaged, there was little they could do: the issue had to be settled in combat's crucible.
Now, did that mean Lincoln shied away from prodding his generals in between fights? Heck no! Lincoln's telegrams to McClellan before and during the Virginia Peninsula campaign (June 25 - July 1, 1862) are legendary. Lincoln had already named corps commanders for McClellan when the general dragged his feet about it (a move that showed Lincoln's growing impatience and willingness to step in), and had been harassing McClellan for literal months to move faster in his approach to Richmond. Lincoln had also countermanded one of McClellan's orders by holding Gen. McDowell back from the Peninsula Campaign because the promised number of defenders for Washington hadn't been provided (despite McClellan's assertions that they would be).
You can see, then, that by the time of the Peninsula Campaign, Lincoln was already exerting a considerable amount of control over McClellan and his dispositions. When he sent the telegram below, he came as close to outright ordering McClellan to attack as he ever did throughout the war (much like OP's question). Lincoln wrote to McClellan on April 9, 1862:
"And once more let me tell you, it is indispensable to you that you strike a blow...The country will not fail to note -- is now noting -- that the present hesitation to move upon an entrenched enemy, is but the story of Manassas repeated. I beg to assure you that I have never written you, or spoken to you, in greater kindness of feeling than now, nor with a fuller purpose to sustain you, so far as in my most anxious judgment, I consistently can. But you must act."
In other cases, the problem wasn't that generals were failing to be aggressive enough, it's that they were too aggressive. Pope got into bad trouble at Manassas pt. 2 when he assumed that he had trapped the Confederates (rather than the reality, which was that they had laid a trap for him). Likewise, Hooker was so confident that he'd engineered a perfect campaign against Lee near Chancellorsville that he left his army open to a crushing flanking attack by Jackson (which nearly destroyed the Army of the Potomac). There were other generals that Lincoln prodded into more offensive postures, like Rosecrans, but there again one can see the danger of giving a general broad, aggressive orders without thought to other outcomes. If a general doesn't handle their army correctly and isn't in tune with what the enemy is doing, all the aggression in the world won't help.
[Sources: Bruce Catton, 'Mr. Lincoln's Army'; Doris Kerns Goodwin, 'Team of Rivals']
Thank you for your answer.
I was aware of Lincoln's impatience when he said (paraphrased) "if McClellan isn't going to use the Army of the Potomac perhaps I could borrow it for a while". But I didn't know to what extent he took matters into his own hands and why or why not.