A much better insight is in
Chapter 26 of Carman's Maryland Campaign.
Militarily, the situation was roughly (a repost):
If you read McClellan's personal letters he has a sense of foreboding that Pope was going to be destroyed. He personally thinks his forces can save Pope, and wants to get them to him. However, Halleck literally has no idea where Pope is, and so McClellan doesn't know where to send them.
Here I should note that the only communications between Pope and the outside world are because of, and via, FJ Porter. Porter landed at Aquia Landing and found Burnside there. Burnside had been ordered to send forward the bulk of his force but had been forbidden from going himself to Pope, like McClellan was a few days later. Porter arranged to send couriers back to Burnside who would forward the news up to Washington. Even this route became compromised.
When McClellan landed it was at Aquia, where 2nd Corps landed. 6th Corps had landed at Alexandria. Everything is confused. Halleck is trying to communicate directly with 6th Corps and failing, directing a botched movement by a brigade and a half against Bull Run Bridge (this force, under Taylor, runs straight into AP Hill's Division and is smashed). Franklin, Smith* and Slocum had all left the corps and headed to Washington, leaving Hancock in acting command. On the morning of the 26th, McClellan secures permission to go to Alexandria himself and find out what is happening and goes. Arriving at Alexandria he finds chaos - the corps and division commanders are missing and Halleck is spewing out nonsensical orders to brigadiers. After reordering the situation McClellan grabs a gunboat (USS Ariel) and heads to Washington to confront Halleck directly.
What we know about said meeting comes mainly from Halleck's report. McClellan arrived at Halleck's house (ISTR ca. 0100 hrs) and got him out of bed, demanding Halleck actually take control of the situation. McClellan then rounds up the errant Franklin and his division commanders and returns to Alexandria the next day. His orders from Halleck as of the 27th were to hold fast at Alexandria and to pull in the 2nd Corps (from Aquia), 4th Corps (from the Peninsula) and Cox's division (also at Aquia).
On the afternoon of the 28th, probably after a bollocking from Lincoln and Stanton, Halleck changes his orders again - 6th Corps will march to Pope. This leads to the obvious question of "where is Pope then?". Halleck has no answer but rather pathetically orders McClellan to "find out". Hence McClellan orders 6th Corps to advance the morning of the 29th. Reaching Annandale the lead division commander (Smith) goes firm and asks should he advance further. McClellan simply refers this up via the wire to Halleck, who leaves it upto Smith. Smith does exercise the option that Halleck allowed to him.
The next day (30th) McClellan sends 2nd Corps forward as well, and 6th and 2nd Corps edge their way blindly towards the sound of firing, and Franklin is forming his corps from column into a fighting line along the Cub Run just as Longstreet is hitting Pope's hanging flank. 6th Corps acts as a rearguard, withdrawing to Centreville after Pope's army is past.
The major issues regards said movement were that Halleck literally had no idea what was happening. If he'd simply known where Pope was he could have directed McClellan where to send the forces, but he didn't. The 6th and 2nd Corps had to edge forward in an "advance to contact" rather than marching through a safe rear area. I think this map (which Ned Baldwin has modified) shows the issue succinctly:
View attachment 303743
Jackson's corps is between Pope and Franklin. It is actually impossible for Franklin to reinforce Pope, as Lee has already enveloped Pope completely. The question becomes one of an unsupported attack against Jackson independent of Pope.
* Since writing this years ago I've learnt that Smith, and apparently Franklin and Slocum, had departed the army to try and wangle postings to the western army. Smith was told in no uncertain terms by Stanton that he could be reassigned to the west if he wanted, but that the promotion to Major-General that McClellan had recommended would not be confirmed in that case.