The only places Wallace has a reasonable shot at are Tennessee and South Carolina, which knock Nixon down to 282. The only other place where he has even the tiniest chance is North Carolina, but that probably requires a North Carolinian VP- and even then, Nixon has 270 votes. So Wallace needs one faithless elector, then Nixon is 1 short at 269.
As to what happens, well Humphrey's president but one totally lacking popularlegitimacy(he recieved fewer votes both electoral and national then Nixon, and the Wallace voters were predominantly Nixon-preferring as well). I half suspect an amendment stating that the popular vote determines the winner will be passed in reaction.
I suspect Humphrey wouldn't achieve much, though he would wind down Vietnam earlier.