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The entire platform is at the link above, post 1 in The Constitution Party on the War on Terror. The quote isn't selective, but I'll post the entire preamble below. It's why they pick up support from some of the unsavory places Paul does. Folk like their Senate candidate in Delaware Mark Dankoff, who ironically writes for Willis Carto, as Paul does, and is on Republic Broadcasting, ironically run by the same fellow who gave Alex Jones his start. The want to scrap the income tax, a big Paul issue, though they plan on replacing it with tariffs and excise taxes. With the exception of they're contension that the Panama Canal is sovereign US territory, I suppose we'll invade, they're a good fit for Paul and he could easily add a tenth or two percent to their normal 0.3% or so of the vote.

I don't think the LP appeals to nutballs the way the CP, but clearly their support for a Paul candidacy (he can run on both tickets), brings that into question.

Preamble
The Constitution Party gratefully acknowledges the blessing of our Lord and Savior Jesus Christ as Creator, Preserver and Ruler of the Universe and of these United States. We hereby appeal to Him for mercy, aid, comfort, guidance and the protection of His Providence as we work to restore and preserve these United States.
This great nation was founded, not by religionists, but by Christians; not on religions but on the Gospel of Jesus Christ. For this very reason peoples of other faiths have been and are afforded asylum, prosperity, and freedom of worship here.
The goal of the Constitution Party is to restore American jurisprudence to its Biblical foundations and to limit the federal government to its Constitutional boundaries.
The Constitution of the United States provides that "no religious test shall ever be required as a qualification to any office or public trust under the United States." The Constitution Party supports the original intent of this language. Therefore, the Constitution Party calls on all those who love liberty and value their inherent rights to join with us in the pursuit of these goals and in the restoration of these founding principles.
The U.S. Constitution established a Republic rooted in Biblical law, administered by representatives who are constitutionally elected by the citizens. In such a Republic all Life, Liberty and Property are protected because law rules.
We affirm the principles of inherent individual rights upon which these United States of America were founded:
That each individual is endowed by his Creator with certain unalienable rights; that among these are the rights to life, liberty, property and the pursuit of happiness; That the freedom to own, use, exchange, control, protect, and freely dispose of property is a natural, necessary and inseparable extension of the individual's unalienable rights;
That the legitimate function of government is to secure these rights through the preservation of domestic tranquility, the maintenance of a strong national defense, and the promotion of equal justice for all;
That history makes clear that left unchecked, it is the nature of government to usurp the liberty of its citizens and eventually become a major violator of the people's rights; and
That, therefore, it is essential to bind government with the chains of the Constitution and carefully divide and jealously limit government powers to those assigned by the consent of the governed.