I don't know why people are rushing to explain that Democrats lie too, about other things, or that politicians in general lie. The question can be taken at face value: given that we all agree that all politicians lie and that Democrats lie in ways that arguably create a moral equivalence, why do Republicans lie about debt and spending in particular? (rather than about other things?)

It is a fair question. Of the many things Republicans lie about, debt and spending is probably where they lie the most. The reasons are:

1. It is an important current issue given the state of the economy, so it is worth lying about.
2. The "experts" (economists) are in the doghouse currently and nobody trusts them. Not even liberals. So there is no authority to appeal to who might contradict lies (unlike in the case of say, creationism, where biologists have not lost authority). So debt and spending are safe to lie about.
3. Debt and spending rhetoric applies most directly to government actions and their failings. By contrast talk of "fraud" will stick most convincingly to Wall Street bankers. Talk of "greed" will stick best to business owners. All three are actually aspects of the same issue (notice how liberals mostly lie along the "fraud" vector of economics and to a lesser extent along the "greed" vector?). Since Republicans nominally hold "Big Government" up as an important enemy in their grand narrative, any attack on government is strategically helpful, since it motivates later cosmetic efforts to "shrink" it in favor of "individual autonomy" thereby preserving the narrative. So the subject is strategic to lie about.
   
4. When you try to understand the economics of nations using metaphors of family or individual finance (a terrible idea), debt and spending naturally map to irresponsible and morally dubious behavior. So using dubious analogies (like that financially illiterate Facebook image that did the rounds showing America's finances naively mapped to household finances), the subject becomes easy to lie about.
5. Finally, actually understanding why debt at the level of nation states is not the same as debt at the individual level requires mastery of rather abstruse economic ideas and an understanding of the disagreements between Keynesians and Friedmanites, tradeoffs between debt and inflation etc. This takes some education. Which means that refuting extremely simplistic arguments about debt is very difficult. So false claims are difficult to refute in ways that convince less educated people.

Items 1 and 2 actually apply to Democrats as well. So the real difference is in items 3-5. I assume 3 is self-explanatory, but it may not be easy to see why 4 and 5 help Republican politicians more than Democrats.

Item 4 first.

That the analogy to family or individual finances is deeply flawed doesn't make it less effective. In particular, it easily conjures up imagery that offends the moral sensibilities of conservatives (quick, think up an individual like yourself, but who has run up a lot of debt and continues to spend like crazy, does that person seem responsible or worthy of help?)

The analogy does not work as well on liberals because liberals are more likely to focus on differences within society and debt and spending as a way to address social justice concerns. This mental model (equally flawed as a way of understanding national debt) does not immediately conjure up images of profligate excess. It serves instead to highlight compassion.

By contrast, Republicans are more likely to perceive national identity (an "American character") in monolithic ways, and are more likely to have a canonical mental model of an "American individual/family" in their heads to whom they can immediately map indebtedness and spending as moral failings.

If America the country metaphorically maps to a middle class white family to you, debt and spending map to an irresponsible and lazy middle class white family. If on the other hand, America the country maps to even two families to you (one white and privileged, the other black and oppressed with the dad in jail) the debt and spending issues immediately become harder to map down via analogy to individual behaviors. So the rhetorical strategy fails. This is why Democrats don't use it.

Item 5: since Republicans in general are less educated than Democrats, refutations that rely on somewhat advanced college-level economics are more likely to convince Democrats. This one is a straightforward effect of demographics.

Full disclosure: I am mostly a centrist on 99% of issues, and tend to agree with Republicans on many key things. This is the first time I will be voting in America (or ever) and I am leaning Obama primarily because this election has come down to personalities for me and I just don't like what I've seen of Romney. If the candidates were swapped around, I'd vote Republican.

But hopefully not because the lies about debt and spending actually work on me. I am susceptible to completely different lies.