How much does it cost to deal with i've got a huge tree right up against my house?

Priced by access and by what sits underneath, not by the tree. Anything over a roof must be rigged and lowered rather than dropped, which is slow, so the same limb costs a multiple of what it would in open lawn. A back yard a bucket truck cannot enter means climbing, and more hours. If removal is genuinely warranted, proximity to the structure is the single largest multiplier on the estimate — crane setup, roof and gutter protection, sometimes a fence panel removed for access — which is also exactly why 'it's close' gets quoted as a removal so often.