My rough read on the situation as of the early afternoon is that, from McClellan's point of view, Burnside now has the bridge and he can feed 9th Corps over it and get them attacking. In addition to that actual attack, it forces Lee to react; if Lee has at least enough strength available facing south or in reserve to fight Burnside head-on, then when Burnside advances he will have to have them doing that. At the same time he must hold the centre facing Sykes, and in the north McClellan has the assets to potentially make another attack. That is the threat posed by Franklin's corps.
McClellan can reinforce one of those threat axes that he is presenting Lee with with Morell's division (only). And he has to be quite sure that any attack he launches will at least cripple Lee's offensive capacity - Burnside could at least fall back to the bridge, but if he exhausts 6th Corps then 2nd Corps behind them (for example) could really be in for it if Lee advances.
However, until McClellan does commit Lee has to hold a front line (as noted) and so those forces can't be facing south against Burnside.
In that light I think McClellan's working assumption is that Lee's nearly out of reserves and under severe strain. McClellan ultimately decides to commit Morell on the right rather than the centre, but either way the basic plan seems to be to attack all along the line with all the fresh troops he has left so long as he can attack all along the line. (Sykes' division links up with 9th Corps, at least by my understanding, before AP Hill caves in 9th Corps.)
Basically under these circumstances so long as at least one of those three attacks works, so long as the other two do not collapse before then the result is a Union victory (albeit maybe not very decisive).
But as soon as one of the attacks fails (9th Corps, and it seems to have collapsed quite suddenly) the dynamic is no longer really in place. The assumption that Lee is nearly out of reserves is suddenly much more tenuous, and importantly anything that was previously facing south can be reoriented to face north.
I think McClellan probably knew AP Hill (or a body of troops that we know was AP Hill) had arrived, and we actually to my recollection have records of Burnside/9th Corps being warned by the signals guys. So whatever Lee had facing south at about 12:30 can now be reoriented to face north; the situation is significantly worse for an attack.
Worse, at that point there's guns firing to the northwest. We know that's Stuart's flanking move at New Industry being stopped, but McClellan doesn't yet.