Excellent short summary; thanks. Two points I see somewhat differently:
1) There is nothing fiscally conservative about the effort to "eliminate as many taxes as possible." Rather, the term has been twisted to embrace, oxymoronically, Reagan's "supply-side" economics that displaced true fiscal conservativism from the core of the Republican Party under Reagan and remains dominant.
2) Populism was historically linked with the Democratic Party, not the Republicans. But it has long since degenerated from a broad national political movement in the late 19th century to nothing more than a political "style," consisting mainly of anti-elitism, usually angry, whether from the left or the right. We're hearing that kind of rhetoric now from every Republican candidate attacking Romney from the right. But only one of those candidates has an ideological affinity with the Tea Party. That's because what the Tea Party has revived among Republicans is not a populist segment, but a so-called libertarian one.
Republican libertarians differ from those you've described as fiscal conservatives mainly in their ideological opposition to government entanglement with and privileging of "big business"; for example, government-sponsored enterprises (like the federal mortgage companies "Fannie Mae" and "Freddie Mac" and Federal Reserve Banks), corporate welfare and bailouts for private corporations deemed "too big too fail" (investment firms and the auto industry), and, for some, the military-industrial complex.
The corporate interests that have to some extent coopted the Tea Party are those that stand to benefit from a reduction of the overwhelming political and economic power of the financial sector; hence their affinity with Ron Paul's brand of capitalist libertarianism.
All that said, I think your description of the tendencies within the Republican Party gives the necessary background for understanding the current divisiveness within the party. But I don't think you've answered what I understand to be Smileystr's question: Until now, these different groups of Republicans have generally cooperated in relative peace within the broad coalition of the party. Why have they emerged - or rather, diverged - with such divisiveness now?
I'll address that in a separate comment.
There have always been divisions in both parties. The biggest rift is between social conservatives and fiscal conservatives. Social conservatives want a federal government that encourages moral choices and outlaws or discourages immoral ones. They want religion to play a bigger role both in people's private and public lives and often feel that they in their particular time and place in history are chosen by God to lead the world to righteousness. Fiscal conservatives want a small and limited federal government, balanced budgets, to eliminate as many taxes as possible, deregulate industries and the economy, and free trade.
There are also the neo- vs. paleo- conservatives. Paleoconservatives want what they see as traditional values from a real or imagined time in our past. They tend to be for states rights, isolationism, and protectionism and against multiculturalism, affirmative action and womens and minority rights. Neoconservativies have many liberal viewpoints and often come from liberal backgrounds. After Reagan won the presidency in 1980 he had many Democratic supporters who were known as "Reagan Democrats." Reagan Democrats now form the much of the neoconservative wing in the Republican party. Neoconservatives advocate an aggressive interventionist foreign policy, support wars to promote American interests, and want to spread American style capitalism and democracy to the rest of the world.
There used to be a large populist segment within the Republican party but that segment has been shrinking in favor of more ogliarchy. The Tea Party Movement has re-awakened this segment somewhat though the Tea Party Movement has been largely cooped by corporate interests.
Most Republicans are eclectic and take some positions from each branch of the party but in general identify with one branch more than the others.
See filletofspam's answer for general background about the several political tendencies with the Republican Party. But why have those differences become so much more contentious in this campaign than previously?
The current Republican rifts have been shaped mainly by disillusionment with George W. Bush's big-government, deficit-happy, militaristic presidency, and the financial collapse and electoral disaster it led to. That's what has given "fiscal conservatism" (at least in name) its current centrality, boosted the fortunes of Ron Paul's isolationist-libertarian candidacy well beyond the support for his 2008 run, and, above all, generated such heated opposition among "true conservatives" to Romney's "establishment" (corporate-state) conservatism.
Tax cuts are meant to cause budget deficits. Grover Norquist outlined his strategy of "Starving the Beast." Norquist noted that entitlement programs are popular. Most Americans like Social Security, Medicare, Medicaid, the VA, Pell grants, unemployment insurance etc. Even those who don't use them are glad they are there for if or when they or loved ones do need them. Norquist suggested that running on a platform of cutting popular entitlement programs was a loosing strategy and instead politicians should run on a popular platform of tax cuts that would lead to not being able to afford the programs they are opposed to. Every battle over taxes is a battle between those who oppose entitlements and those who favor them.
I'd say the divisions in the Democratic party are even farther apart. While most Dixiecrats have become Republicans due to Democrat LBJ supporting the Civil Rights Act and because of the Republican Southern Strategy of opposing civil rights there is still a significant conservative wing in the Democratic party. There hasn't been a liberal or progressive wing in the Republican party since the 1920's.
There is no "far left" in mainstream US politics. The Democratic party would be considered conservative nearly anywhere else in the civilized world and the Republican party would be considered doctrinaire conservative extremists.
I would love to talk about this and help you out, but it would really take a long, long, long, long, long time, and it's quite complicated. I'm not saying that you wouldn't understand, rather it's a really big can of worms to open and we could be here for the rest of our lives. I'll say one thing, just because a person "belongs" to a party, doesn't mean that they all agree. People are individuals. Politics is a very strange bird and to understand it is not very possible. You can only follow it.
I'll answer to liberal when I'm in a generous mood, but I don't "like government" any more than I like business. What I like is for people to recognize and affirm each other as beloved sisters and brothers as we come together to participate fully in all the decisions that affect our lives, whether in governance or in production and allocation of resources. Today's "populists," whether they are fearful or angry or both, are all over the political map, with no shared vision or program.
There are divisions in all parties including the Democratic party. There are centrists and there are far right and left people. I was a Republican my whole life but am actually thinking od voting for Obama this year because of where capitalism is heading. Still a good system, just needs some checks and balances. Plus i like what the Obama administration is doing when it comes to our indiginous peoples.
The Tea party has its roots in libertarianism though it has always been eclectic. My observation of a populist view comes from observing that many in the Tea party distrust both big government and big business. As I see it: Conservatives fear big government but like business. Liberals fear big business but like government. Populists fear both.
Same thing that causes it in all parties everywhere....self interests, power, greed, and control.