There are two key pillars to Nazism, that being Nationalism and Socialism. Nationalism wasn't always the domain of the Right. Those on the Left in America used to also be nationalists. It wasn't until the latter half of the 20th century that nationalism became a dirty word on the American Left.
Socialism, which from a traditional American view is clearly Leftist, permeates Nazism. Even their nationalism is promoted through socialism.
I absolutely agree that in America today there are few on the Right which are actually traditional, or paleo-conservatives. With much of the Right giving in to the advances of the Left, they have attempted to meld a bit of their Rightist philosophy with Leftism. This gives us so-called conservatives who are "fiscal conservatives but social liberals".
Meanwhile, as the Right moves more to the Left, the Left moves even further to the Left. True conservatives from the past would be viewed as extremists by most on the so-called Right today while past Leftists would be viewed as to conservative for the Leftists.
This is why today we can have those like Romney and Christie hailed as conservatives and we hear those to the right of them tagged as "far right wing", "extremists", and worse.
This is also why some Leftists today think Hillary Clinton isn't Left enough though in the 90s she was considered a far Leftist.
The term "conservative" is basically meaningless in America today. A true, traditional constitutionalist today couldn't be a conservative because there is nothing of that left to conserve! Nearly everything the conservatives have claimed to be fighting to conserve for the past several decades has been lost. This is why we see todays conservatives working to conserve the welfare state, to conserve big government with tiny reforms around the edges to suit their ideas, to conserve the influx of millions of illegal immigrants, to conserve unconstitutional court rulings as "settled law", etc.
Nazism isn't conservatism but then again, American conservatism today isn't traditional conservatism either.