Let me list my two biggest problems with compiling to C. If this is a problem for your language depends on what kind of features you have.
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Garbage collection When you have garbage collection you may have to interrupt regular execution at just about any point in the program, and at this point you need to access all pointers that point into the heap. If you compile to C you have no idea where those pointers might be. C is responsible for local variables, arguments, etc. The pointers are probably on the stack (or maybe in other register windows on a SPARC), but there is no real access to the stack. And even if you scan the stack, which values are pointers? LLVM actually addresses this problem (thought I don’t know how well since I’ve never used LLVM with GC).
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Tail calls Many languages assume that tail calls work (i.e., that they don’t grow the stack); Scheme mandates it, Haskell assumes it. This is not the case with C. Under certain circumstances you can convince some C compilers to do tail calls. But you want tail calls to be reliable, e.g., when tail calling an unknown function. There are clumsy workarounds, like trampolining, but nothing quite satisfactory.