No, no a thousand times no; per http://en.wikipedia.org/wiki/501(c)_organization#Types:
There are 27 types of 501(c) organizations, ranging from the familiar "501(c)(3) — Religious, Educational, Charitable, Scientific, Literary, Testing for Public Safety, to Foster National or International Amateur Sports Competition, or Prevention of Cruelty to Children or Animals Organizations" to the obscure "01(c)(27) — State-Sponsored Workers' Compensation Reinsurance Organization".
The fuss here, to my knowledge, is about 501(c)(4) organizations, "Civic Leagues, Social Welfare Organizations, and Local Associations of Employees". Quoting Wikipedia:
"501(c)(4) organizations are generally civic leagues and other corporations operated exclusively for the promotion of social welfare, or local associations of employees with membership limited to a designated company or people in a particular municipality or neighborhood, and with net earnings devoted exclusively to charitable, educational, or recreational purposes. 501(c)(4) organizations may lobby for legislation, and unlike 501(c)(3) organizations they may also participate in political campaigns and elections, as long as its primary activity is the promotion of social welfare. The tax exemption for 501(c)(4) organizations applies to most of their operations, but contributions may be subject to gift tax, and income spent on political activities - generally the advocacy of a particular candidate in an election - is taxable. Contributions to 501(c)(4) organizations are usually not deductible as charitable contributions for U.S. federal income tax, with a few exceptions. 501(c)(4) organizations are not required to disclose their donors publicly."
So, everyone, please, recognize that these are not the theoretically apolitical 501(c)(3) organizations you may be most familiar with (Wikipedia goes into some detail on this) but organizations that are explicitly allowed to engage in political activity, with corresponding disadvantages in losing tax deductibility for it.
To use the example I'm most familiar with, the National Rifle Association, the NRA proper is a 501(c)(3), it runs target shooting, training, safety instruction, a whole lot of apolitical stuff. Their lobbying organization, the Institute for Legislative Action, is a 501(c)(4). They have a separate political action committee (PAC) that following the usual rules donates (now small, since the limits weren't inflation adjusted) sums directly to politicians (which I take to be mostly symbolic, not "buys the politician" ... if for no other reason than few if any stay "bought" :-). And PACs are a type of non-profit organization as well.