My guess, from the text, is that the defense remained stout in the area of the Gate. Only the Black Rider, riding though the broken gate, could have beaten back all resistance. When the Witch-King is driven from the Gate by Gandalf (some think that the Rohirrim horns were what made him break off his attack, but we all know that it's lucky that Pippin showed up when he did to save the Witch-King from Gandalf's staff
), Sauron's forces are no match for Prince Imrahil and his soldiers, who plug the gap with dead foes. Add to that that the sun has risen, and in the books the orcs and other ilk do not fight optimally in daylight.
My guess.