You're certainly right that when you look at government spending and you want to map that from government spending to the implications for inflation, the amount matters, but also what the spending is matters. Different types of spending have different multipliers. Some spending is much more related to demand. Other spending is adding to supply. The more that the spending is adding to supply and not demand, the more it will actually help moderate inflation, so yes, I think to the extent that government spending is augmenting the supply, it will be better for inflation than if it's purely increasing demand.
There are a lot of things you can do on housing. Some of them may go more toward stimulating demand and others may go more toward stimulating supply.