Can i've got a huge tree right up against my house be fixed without removing the tree?

Almost always, and the fix is pruning rather than removal. Clearance pruning that gets limbs off the roof and gutters — with enough separation that a branch loaded with rain or ice still cannot reach the shingles — permanently solves most of these complaints, with a return visit every few years. Removal earns its place when the species is large and structurally poor (silver maple, Callery pear, a dead ash), when the trunk itself carries a defect, or when the entire crown leans over the house with no way to reduce it. 'It's close' is not by itself a removal justification, and you should push back if that is the only reason offered.