On debug builds, it's about evenly split between typeck/borrowck and codegen (including LLVM IR construction and LLVM passes). On release builds, LLVM optimization time tends to dominate everything.

Niko Matsakis is actively working on improving typechecking time--there should be plenty of tricks we can try once we have enough data as to the lowest-hanging fruit. Felix Klock and others are working on reducing the amount of LLVM IR we generate to speed up codegen. There have also been designs for incremental and parallel compilation that will be long-term but have potential for big improvements down the road.

I think with careful work we can get down to a good edit/compile/run experience. Compilation speed probably won't ever be as good as a direct-to-assembly compiler for language with an extremely simple type system with no real IR for optimization would be, but I don't believe there's a magic bullet that will beat LLVM's compiler performance while providing excellent optimization, and for Rust's goals we need the runtime performance.