Republican and Democratic orthodoxy
Orthodox Republicans accept all or most of these positions
1. No income tax income increases for the rich.
2. Do not believe in human caused global warming, or simply do not want government trying to manage the problem.
3. Believe in only limited government regulation on businesses except when it helps your bottom line.
4. Believe in maintaining a strong national defense-this one never changes!
5. No public financing for elections, and only limited regulation of campaign contributions
6. Do not like unions.
7. Do not believe in universal health coverage
8. Pro-life (though it's OK to not do anything about it, other than appointing conservative judges)
9. Not a fan of academia or of the mainstream news media.
10.No amnesty for illegal aliens, but don't be serious about enough to solve the problem by actually deporting all 11 million of them.
If you can't check at least 9 of these 10 your a Rhino ( Republican-In-Name only). As far as a I know, Sarah Palin & Michelle Bachmann can check all of these. Rush Limbaugh and Sean Hannity would both get perfect scores as well. Rick Perry can check 9 out of 10 (he fails on immigration policy). George W. Bush would able to check 9 of 10 as well. Mitt Romney, has at various points not been able to check at least two of these, though Mitt is trying to lean in a more orthodox direction on most of these items. John McCain fails this test on at least two of the ten though it's unclear as to what his actual score should be.
There are a few other points of orthodoxy (American Exceptional-ism. Gun rights, Enhanced Interrogation), but there begins to be more free thinking when you get beyond these first ten. Libertarians sometimes clash with social conservatives. Less educated populist Republicans clash with Wall street types.
Foreign Policy is a special case. While it's expected that Orthodox Republicans will disagree with Obama's foreign policy, it's probably true that some Republicans might agree with aspects of Obama's foreign policy if a Republican President was carrying them out (For example some aspects of his Libyan and Afghanistan polices). Republicans are little less confident than they used to be on Foreign Policy after the Iraq War. Orthodox Republicans still believe that the Iraq War was the right thing to do , but recognize that they did lose some Independent and Blue Dog Democrats votes in 2008 because of Bush's handling of the Iraq War.
At the present time, orthodoxy favors business conservatives over social conservatives which means that it's OK to not be overly concerned about having prayer in school, or be too worried about gay marriage. And there is some suspicion of Wall Street among some in the Tea Party, which isn't true of establishment Republicans. During the George W. Bush years, there was an indifference to balancing budgets, and a predilection for earmark spending, however now orthodoxy is moving more towards wanting to actually balance the Federal budget as a backdoor way of actually shrinking government.
Republicans have found that orthodoxy works for them, because when they walk in lock step they, can keep their coalition together, seem more principled, and have a more energized base.
What are the litmus tests for being a Democratic politician?
Generally you have to...
1. Favor some kind of attempt at universal health coverage
2. Be pro-choice (it's OK to say your personally opposed to abortion).
3. Be willing to raise taxes on rich people, and be rather indifferent to that fact that the poor and lower middle class don't pay much income tax, though usually taxes of any kind are OK at the state level.
4. Like vigorous government regulation, sometimes even when it is anti-growth.
5. Believe in some form of leniency or amnesty for undocumented immigrants. A particular blind spot for liberals..
6. Support unions, especially teacher unions.
7. Agree that humans cause at least some of the Global warming problem, though this one has gone to the back burner.
8. Be OK with government Stimulus spending, have an inordinate faith in Keynesian economics, and not recognize that businesses create most jobs, not government.
Anybody running for the President in the Democrat party would probably be able to check all these. But there is diversity of opinion- liberals would prefer a single payer health plan. Moderate Democrats like balanced budgets, and establishment democrats are OK with America's role as the world's policemen, while Liberals want us to stop fighting wars. Some Democrats support Israel, some don't.
Democrats have always had more problems with staying in lockstep, because on the Presidential level, voters don't usually vote for liberal candidates, but will vote for moderate Democrats. Obama was the exception to the rule, the first clearly liberal president since at least Lyndon Johnson. It is hard to govern completely as a liberal president in a relatively conservative nation , and Obama has sometimes had to govern from the center, which angers his base, but has done nothing for him with Republicans, or Independents.