Umm... No.... The law defines 501c4's as
(501) (C) (4)
(A) Civic leagues or organizations not organized for profit but operated exclusively for the promotion of social welfare, or local associations of employees, the membership of which is limited to the employees of a designated person or persons in a particular municipality, and the net earnings of which are devoted exclusively to charitable, educational, or recreational purposes.
(B) Subparagraph (A) shall not apply to an entity unless no part of the net earnings of such entity inures to the benefit of any private shareholder or individual.
Politics is not social welfare. Now I agree, these groups can lobby, but they can't engage in electioneering in any way shape or form.
Social Welfare - The well-being of the entire society. Social welfare is not the same as standard of living but is more concerned with the quality of life that includes factors such as the quality of the environment (air, soil, water), level of crime, extent of drug abuse, availability of essential social services, as well as religious and spiritual aspects of life.
Forming a political group interested in electing people who will reform the tax code is NOT social welfare.
If you want to do that, then you should file under 26 U.S.C. § 527 : US Code - Section 527: Political organizations