The Republic party doesn't work that way. Look at what it did with its health care proposal in the Senate. Supposedly there was a committee of 13 - but when the plan was hatched, only a couple of Mitch's buds had anything to do with it.
The Republic party wants one set of rules for itself and another set for everyone else.
Of course, the best thing that could happen would be the abolition of all political parties. Just ask George Washington.