The Spartans have a miraculous habit of having religious holidays or poor omens interfere with potentially costly military obligations. Suffice it to say, a POD that produces a full mobilization is likely to be large indeed, to say nothing of unlikely in the summer of 479 itself. Sending the entire army to oppose the Persian seemed a legitimately risky proposition before Thermopylae and more importantly before Salamis.
Nevertheless, I'll take the WI at face value and go from there. First question, just how many Spartans do we mean? While estimates for the number of Spartiates in 479 are iffy, I've heard as many as 8,000. That's probably a bit much to expect the Spartans to send (someone has to stay home). For simplicity sake, let's assume the Spartans send to Thermopylae the contingent they sent to Plataea. That's 5,000 Spartiates, 5,000 Perioikoi, and 35,000 helots. OTL there were also 12,000-13,000 other Greeks defending the pass before the Spartans made their last stand. At Plataea, there were as many as 60,000 additional Greek troops to complement the Spartan army. Now, certainly if the Spartans send substantial numbers of troops, more Greeks will come than came to the pass originally, but assuming the full contingent may be a bit much. We may get a better idea of a more plausible number if I could remember the number sent when they were thinking about making a stand in Thessaly (about where Heraclea Trochis was built), but that number wouldn't be "WI the Spartans sent everything they had."
Given the extreme confines of the pass at Thermopylae, a force of say 60-70,000 total Greeks could make quite a wall. Even if Herodotus' total number of Persians is accurate, the force at Thermopylae is only 250,000 to 300,000. Probably the number is much smaller, maybe twice the size of the Greek force. The problem is I'm not sure what the maximum number of troops that could fight at any one time would be.
Another problem is whether Xerxes continues to send troops against the Greeks if their numbers are so larger. They may have enough reserves to keep the pass blocked nearly indefinitely. This probably ensures he tries to find a way around, if he's insistant on breaking through (which I think he probably would be). But can he get enough troops around the mountain pass to rout the Greek force? This is the big question, in my mind, and heavily depends on the precise lay of the land. I'd guess that Xerxes might try it, but find himself surprised by the number of Greeks he finds. The Greeks discover that one can fight in a phalanx in a square and may do a fairly good job holding out, since the strength of a phalanx would be increased the more firmly packed and motivated the troops were. After this attack is repulsed, Xerxes probably withdraws.
But of course the story doesn't end there. The Battle of Artemesium probably drags on. The Greeks (particularly the Athenians) won't be dis-spirited and won't withdraw. Xerxes needs to force his way through and may be thinking about using his navy to land troops in Attica and force the Spartan lead force to withdraw. While the Greeks did prevail at Artemesium OTL, the Battle was much closer than Salamis and saw far higher Greek casualties, particularly among the Athenians (who were defending their homes for all intents and purposes). If the Greeks prevail at Artemesium, it may be at the expense of the Athenian navy, which may be decimated by the struggle. And even so, I'm not sure the Greeks win: Themistocles may not be dominant enough yet and the Athenians will not now the harbors as well as they did Salamis. Hence, the result is either to scuttle the power of Athens (which probably has a much larger degree of class conflict without the events preceeding Salamis and whose navy may not become the back-bone of Greek victory) or a Persian victory at sea, which would leave the Greeks very troubled. If things go largely as OTL, save for the events of Salamis, then the history of Athens itself will be far, far different.