Can a dynamic language like Ruby/Python reach C/C++ like performance?

I wonder if it is possible to build compilers for dynamic languages like Ruby to have similar and comparable performance to C/C++? From what I understand about compilers, take Ruby for instance, compiling Ruby code can't ever be efficient because the way Ruby handles reflection, features such as automatic type conversion from integer to big integer, and lack of static typing makes building an efficient compiler for Ruby extremely difficult. Is it possible to build a compiler that can compile Ruby or any other dynamic languages to a binary that performs very closely to C/C++? Is there a fundamental reason why JIT compilers, such as PyPy/Rubinius will eventually or will never match C/C++ in performance? Note: I do understand that “performance” can be vague, so to clear that up, I meant, if you can do X in C/C++ with performance Y, can you do X in Ruby/Python with performance close to Y? Where X is everything from device drivers and OS code, to web applications.