Well despite the policies of Bush, I had always thought that the Republican party was accepted as a party of small government, or at least genuinely trying to espouse that ideology even if it didn't happen in reality. I was simply curious as to whether the parties had their modern views when they were founded, or whether they were in fact more similar to the labels the OP described, but having changed since then.

On an off-topic note, I feel I have to post this, possibly the most odd political party I have ever seen or ever will see:

Spoiler Alert, click show to read: 
Libertarian National Socialist Green Party - Politically correct Nazis? These Libertarian Green Nazis are either the strangest conglomeration of diametrically opposed political ideologies of a political party I have ever seen -- or one of the most wry political practical jokes found anywhere on the net (I'm not certain which conclusion is correct, but I strongly suspect the latter). This party purports to be comprised of atheist, peaceful, pro-gay, pro-drug legalization, anti-racist, environmentalist Nazis who acknowledge the Holocaust likely occurred (but are neutral as to its justification) and oppose the government sponsored killing of Jews, Christians & gays and the disabled. The LNSGP "rejects Judeo-Christian moral standards, victim mentality political behavior, capital-centric value systems, and authority." While membership is open to anyone regardless of their race or sexual orientation, individuals who openly profess a belief in either Judaism or Christianity are denied party membership. Articles, platform, FAQ and graphics. Worth a visit -- even if only to decide for yourself if this is a joke or if it is serious. In the past -- and as an indicator that the LNSGP is probably a practical joke -- the LNSGP's site had sections dedeicated to claims of participation in a public service project named the "Jewish Community Brothership" (to "Communicate the modern interpretations of Nazism and its implications for Jews in today's multicultural Reich") and some links to very bizarre "news" articles (example: "Nazi Moon Bases Established in 1942").