The problem is that the modern Republican party is built on a Fusion Conservatism and a form of Conservatism altered and crafted as what it is, and required to be what it is, from various interests tacked on and various fusionisms. That is why I don't just talk about Conservatism when I need to be specific, but specifically call it the Modern American Conservative Movement (Or MACM, which I pronounce as Jay Sherman would). Don't mistake the shorthand as an attempt at a derogatory/dismissive term, by the way; it's only a shorthand so I don't have to write the whole thing out. A belief in limited government and low taxes does not also require a belief that global warming and evolution are a scientific hoax or otherwise wrong or that Liberalism equates [Insert Worst Negative]. In the MACM, they both tend to be believed. It's a very complex and often tangled web which has created Conservatism and the Republican party as an ideologically unified powerhouse of politics, and has allowed for such things as low income people fighting for tax cuts for the wealthy and complaining that poor people just aren't working hard enough. It's what you get when you mix economic conservatism with social conservatism, with traditionalism, with classical liberalism and with all those various other things. The people involved therefore don't have each other's interests much of the time, but adopt them anyway under mutual fears or dislikes and/or some understanding (conscious or subconscious) of scratching each other's back, or that was the initial understanding which has long since been forgotten by subsequent generations who just hold the ideology of the MACM because that is what they were raised with.
The Democratic party does not have such a thing, and I think it would be difficult to get it to. As it stands, the fact that limited government equates with denying climate change and other scientific fact is very queer and the mutant child of an odd socio-political puberty and maturity of the Conservative Movement in America. It's chief purpose seems to lay in economic conservatism: a denial because how can Free Market Capitalism produce negatives? It's prosperity as an idea seems to come from things such as distrust or dismissal of intellectuals, potentially tied into distrust or dismissal of science where it also has supported evolution. You could also tie in the rejection of blame due to feelings of being blamed and ire at it which is strong with Conservatism. White males and White people in general were strongly pushed into Conservatism during the 60s and 70s because the various movements targeted the "establishment" and blamed it or were perceived by segments of the population as doing such, and the fact was the establishment was White men (also White people in general, so White women, but mostly White men). This created a psychology of resentment, and also a feeling that because these White people who felt they were being blamed were not always so well off and did work hard that the people blaming them were just lazy or ungrateful or otherwise wrong in an adversarial way, and has created a knee jerk anger and rejection of anything that is felt to be blame and an attack and rejection of the perceived blamers. And there's all the assorted tangling of psychological factors and interests which I would have trouble outlining cohesively. It's literally a college thesis worth of explanation and discussion.