I don't know, a lot of the English nobles were Anglo-Danish by this stage and the Normans were seen as troublemakers, their foothold gained because Edward the Confessor liked them. Plus they were viewed as militarily weak, unlike Harald who was a proven warrior. Oh, William was raiding southern England, burning, pillaging, etc, once he landed. he was no better than Harald in that respect.
As to Tostig, he was hardly a model of virtue prior to 1065, infact Harold on a couple of occasions moved to have his brother lose his lands and power; Tostig was only saved because Edward stood up for him, partly to annoy Harold but also there is an idea that Edward actually liked Tostig.
Given Hardrada's record in prior conflicts I suspect that most Saxons would have preferred William as being likely to at least honor the terms he offers. As opposed to a guy who suddenly lands in the north of England and torches a town just to show everyone that he's there.
It IS an interesting period, as noted in 1066, The Year Of The Conquest, this period of 32 days where if anyone had pushed even faster or delayed just a bit all of English history might have been transformed.
The book also makes the suggestion that Tostig's behavior and character for 1065-1066 was so different from most of his life that he may have been suffering from some kind of mental problems.