So--if personally controlled demesne land were not a factor, or more to the point in this era where it is, he decided to count on his status as King, the king who fought off two invasions in fact, to recoup his personal relative standing, he'd have held back and accumulated adequate force for better chances of victory.
Now, as the OP says, he does as OTL (LordTerra's point accounting for the "mystery" of "premature attack") and his army is mauled as OTL, but he himself happens not to fall. If he retreats and recovers most of his surviving forces from Hastings (presumably some will desert or be scattered) and waits for more forces to arrive, what are his chances now that 1) he's lost a lot of men 2) to achieve a given balance with William he must wait longer 3) the maximum accrual of force he can hope for is less than if he had held off in the first place and 4) William has longer to do damage, acquire loot, and regroup and rest himself (or strike out to spread out and do more damage). To be sure William has also lost some men and unlike Harold has no immediate sources of more, unless he can pick up English defectors. But he does have the momentum of having won the last battle. This adds to the daunting effect of papal blessing on his invasion and allegations of bad faith on Harold's part.
How will Harold's forces perceive his losing the initial battle? Will it vindicate William's claims, or will knowledgable English leaders and an unguessable amount of the mobilized masses give Harold credit for having had to run from the other end of the kingdom after defeating another feared invader handily, and understand his motives in jumping in at the first moment instead of waiting to muster overwhelming force, and forgive him and rally to him?
I guess a lot depends on just how popular a monarch Harold was. If the English group up as one behind him, England's chances are better; if Harold is liable to be undermined by ambitious rivals who smell blood in the water and think they can cut a deal with William, the Wessex line may be doomed anyway. Note the latter might lead to a better outcome for the English than OTL (if in my opinion still worse than if Harold could repel the invasion completely)--if William knows he needed a lot of defector English lords to win, the Norman kingdom would be more balanced between Norman and English lords; the harrowing of the north might not happen for instance. (Or things could be worse; having promised his co-invaders to divvy up England among them, unless these are terribly decimated he has to choose between betraying his fellow Normans versus betraying some Englishmen of dubious loyalty to him--guess which way he goes!)
If Harold is popular, I daresay that after a second victory defending the land his lords will, albeit grudgingly, acquiesce to measures he takes to recoup his fortunes for the good of the kingdom, at least if these measures are not overbearing and reasonably fair. He might be forced to "modernize" his rule a bit, shifting from being the biggest lord among lords to something more national, shifting revenue from his own demesne to taxes on the realm as a whole--which would be an added burden to relieve some from the immediate victims of William's plundering, but could be sold as the price of a viable defense without which all English would suffer eventually anyway--if only they could know the outcome of OTL and compare!
So anyway along side moral factors such as these, there is the question of how fast Harold can gather additional forces, and set against the more advanced order of battle (if we can call it that) of the Normans (with their fixed and with battles the English can at least survive if not win outright, dwindling numbers) can he draw in enough fast enough to have a good chance of slowing and then stopping and defeating the Normans?
Emotionally the answer I want to hear is "yes" (although that costs us Chaucer, Shakespeare, Elizabeth I, and the gloriously patchwork language that is modern OTL English). But I have no real idea. I'd think a whole kingdom like England ought to be able to beat a duchy, even a duchy reinforced by Flanders, but to be sure a lot of the power Harold can call on is scattered and distant, and the best part that was most mobile, trained, advanced and responsive to his call has already exhausted itself fighting Harald Hardrada, making a fast forced march south while still recovering from that battle, and now been decimated again thrown prematurely into the fray without time for rest or planning. Given his whittled-down core (which also had time limits on service set by law, much time of which has been run out already--in the emergency one would hope they'd waive that and stay with him until the matter is resolved, but one reason for the limits was that the harvest would suffer if the men don't return to the land in time) and that reinforcements would be thinly supplied, late in coming and poorly trained and equipped compared to his best, clearly William has got some shot and will not give up easily. Indeed if it takes Harold too long to concentrate enough force, William may be able to reinforce either by summoning more aid from overseas (inviting in new allies perhaps, such as Brittany maybe? or recruiting local English talent.
So I have to leave this question up to those who can reckon on what additional forces Harold could hope to get, when they might arrive and what quality they would have, versus how fast his interim force would be either bled by William or allowed to decamp, to avoid famine.