(Not a Teacher)
1) Since there are only two parties, that's pretty much what coalition-building means here. However, he may be talking about allying with certain elements of the Republican party rather than try to make friends with every Republican faction.
2) It means Obama intends to set the standard for successful policy-making.
3) Every service branch of the US military wears boots. Therefore, "boots" are a common stand-in for "troops" or "soldiers".