Okay I just rewatched the episode paying closer attention to Team Jonsa's scenes, and this is why the Glovers refused them:
1. This was only the second house they visited and Lord Glover wanted to know how many other houses had pledged support. They lost points for not having more than just the Mormonts.
2. Deepwood Motte was retaken from the Ironborn
with Bolton help. So that's one critical difference right there from the books and why Lord Glover's attitude is different in the show.
3. The Ironborn imprisoned and tortured his wife and daughter and slaughtered their people because they were left defenseless while their troops were off fighting for Robb, so he's naturally bitter toward the Starks for that and not helping them, and expressed it.
4. Glovers biggest objection though was when he found out that their army is mostly made up of wildlings -that completely ended the talks right there!
At the outset of that meeting, Glover did say that he was willing to hear their plea out of the respect he bore for Jon's father.
Team Jonsa gathered support from three houses amounting to a little over 200 men before Jon cut the recruitment process short to march against Winterfell. This is what Sansa complained about at the beginning of the scene at Stannis' former encampment -she wanted to contact another family but Jon insisted there wasn't enough time, probably because the Wildlings and their families are sitting ducks!
There's nothing wrong with that, it is a drama.
If they had shown a bunch of scenes of houses pledging full support and their raising a large army which would crush Ramsay's posse then that's too easy and boring. If that's what they wanted, they wouldn't even need to bother with all that - just change the number of wildlings from 2000 to 10,000! The purpose of the underdog role is to bring in another complication within the "ally" of Baelish who was already set up last season to assume lawful control of the North as its new Warden once the Boltons were deposed.