The basic tenet of the the Republican party (in my eyes) is personal responsibility. The government is not a baby sitter to be handing out goodies to every Tom Dick and Harry that happens along.
Pursuing that line further, since we don't think government should be giving out perks (which are inherently unfair to those that do not receive perks), the government should be smaller. Unfortunately, there are one or two broadly-defined words in the Constitution that are interpreted as giving the Federal government unbridled license to do whatever the heck it wants to (distinctly AGAINST the intentions of the Framers).
Many Conservatives, who also happen to be Republicans, feel that in order for laws to be valid, they must be grounded in morality. Morality is usually (but not always) associated with religious groups, which is why the Christian Coalition types are Republicans. I think it has very little to do with monetary policy and almost everything to do with morality.
Democrats, on the other hand, believe that the government exists to give people a helping hand. They feel that it is morally correct to provide for those who cannot provide for themselves. This is admirable. However, in reality, when you start giving things away, it becomes unfair (as stated above) to give to one group and not to another. Thus a Pandora's box of entitlements is opened which can never be closed (by either side) for fear of angering the ones receiving the services.
This is another reason for limiting the size of government. Government can NEVER get truly smaller, since no politician will risk his career by angering receiver groups. Thus, we need to limit the size of government upfront to avoid (or try to delay) the inevitable growth of government.
As for the issue of WHO should be taxed, I believe most Democrats are a bit delusional. Although most people still pay for their "lockbox"

of retirement benefits (Social Security and Medicare) via payroll taxes, the rest of the government is financed (via income taxes) overwhelmingly on the backs of the successful. This provides a disincentive to success (however small).
50% of this country pays NO income tax. Their beef is usually that their PAYROLL taxes are too high. The same payroll taxes which are actually NOT ENOUGH to provide for their "retirement package" via SS and Medicare.
The problem then arises that these same 50% of citizens do not benefit from tax reductions. They somehow feel it is inherently unfair that those who actually PAY income tax should benefit from a cut in income tax (the "tax cuts for the wealthy" fallacy). They personally see no benefit from a tax reduction, and so think it is unfair that someone else should benefit from one. This is one of the biggest problems with the progressive tax system.
I saw something funny about this on the "No Spin Zone" a few weeks ago. Bill O'Reilly asked Al Sharpton (yes, Democrats actually appear on Fox News) how much of his income should be taxed since he was probably in the upper 1% bracket. O'Reilly asked him if it should be 100%: [Sharpton is paraphrased by me, here] "No", said Sharpton, "I think 75-80% would be fair". O'Reilly asked then if that would be just federal tax, or all taxes combined. "Just federal, the state and local governments need their cut, too".
So where one group is taxed at 0%, Sharpton (and I am sure many other Democrats) want a federal tax on the "rich" to be astronomical.
A quote:
QUOTE
A democracy cannot exist as a permanent form of government. It can only exist until the voters discover that they can vote themselves largesse from the public treasury. From that moment on, the majority always votes for the candidate promising the most benefits from the public treasury, with the result that a democracy always collapses over loose fiscal policy, always followed by a dictatorship.
-Alexander Fraser Tytler
Unfortunately for us, the voters have discovered that they have control of the "largesse of the public treasury".