House does have fascist ideals, at least in the sense of how the economy and whatnot should run. Fascism can be a good thing honestly, Hitler managed to turn Germany from a country that was about to collapse from debt (think Greece today) into one of the strongest nations in the world. If he hadn't declared war on religion and hadn't tried to expand Germany's borders by taking over other countries, Germany might be a superpower by today's standards.
Though I know what you mean, I think you picked a bad example. Though Hitler was given credit for rebuilding his country, he only really sped up what was already happening, and he only managed to do that by excluding Jews, homosexuals and communists from the process, thereby creating more jobs for his first class citizens; hence, arguing that "if he hadn't declared war on religion" (I'm not sure if you mean his hostility towards the Vatican or anti-Semitism, but I'll go with the latter) Germany would have been a superpower is a moot point, since it was part of his strategy to turn it into said superpower.
I find it funny also, House actually has a direct reference to fascism in his dialogue. During pre-WWII, Mussolini's Italy was known as an industrial powerhouse. Their specific quote about it was "Mussolini keeps the trains running on time!" In House's ending cutscene, he says the equivalent of "Speaking of, I really should improve on that monorail, now that the NCR won't be using it. I always hated how it never ran on time", a direct reference to Mussolini. Interesting, yeah?
Fun fact, Italy's reputation as an industrial powerhouse during the war is also fabricated; Mussolini's strength lied entirely on his propaganda campaign, which led to aforementioned quote mentioning that he kept the trains running on time; in actuality, Italy wasn't much of a powerhouse of anything, and the trains ran about as late as they'd ever had, if not more.
I don't particularly think that House's rule would be detrimental because of it being fascist; he's shown to be a shrewd planner and mastermind, orchestrating the rise of New Vegas from its ruins and the downfall of enemy presence in the area (albeit with your help).
My problem is that, given his longevity, his leadership will eventually stale; mental health aside (given how he's already survived this long without going mad) having one leader for extended periods of time isn't good for any nation when said leader is mortal, never mind when they cannot die. I'm aware that House plans on leaving the planet, but the logistics of such a plan are so irredeemably unachievable, especially in a world where most scientific knowledge achieved thus far has been burned in nuclear fire, and all fuel has either been exhausted or is too inefficient to utilize (and one should assume other prime resources are on their way out as well).
House may be a great inventor, but his field was robotics, not rocket science, astrophysics or whatever other fields one might need to realistically pull something like that off.