Good work, folks! It seems that people are (correctly) aligned on D now, but I was asked to comment, so here's my take:

I think what makes this problem confusing is that the words "have" and "do" have so many possible roles in a sentence. Let's clarify things with an example:

I like pie more than my brothers.

What does this sentence mean? Do I prefer pie to my brothers, or do I enjoy eating pie more than my brothers do?

Now, we could clear up this ambiguity by saying “I like pie more than my brothers like pie.” This wouldn’t be grammatically incorrect, but there’s a shorter, more stylish, and more GMAT-like way to say this:

I like pie more than my brothers do.

Here, the word “do” stands in for the idea “like pie.”

Now, what about the following?

I have more love for pies than my brothers do.

Here, we are still using “do” to stand in for the preceding verb phrase: in this case, “have love for pies.” (We can substitute the verb phrase without including the comparative word “more.”) We don’t want to use the word “have”—it would not sound great to say “I have more love for pies than my brothers have.”

So we can already see how the word “do” can stand in for the word “have.” This is NOT the case if “have” is used to indicate the present perfect, as in the following:

I have been going to the gym lately.

Now, if I want to compare myself to my brothers, I will need to use the present perfect for both my verb and theirs. I do this by saying “have” twice.

I have been going to the gym more than my brothers have.

The second “have” (at the end of the sentence) functions just like “do” in the present tense does. It stands for the verb phrase “have been going to the gym.”

As a side note, I should point out that the GMAT often places the second verb BEFORE its subject, like this:

I have more pies than do my brothers.
I have been going to the gym more often than have my brothers.

This is fine, and entails no change in meaning.

Now, back to the original sentence. Here, “have” is NOT being used to indicate present perfect. It is part of the phrase “could have . . . significance.” So let’s write a simple sentence to parallel this one:

I might have more of an impact on the election than do my brothers.

If, instead, I say “I might have more of an impact on the election than have my brothers,” it sounds like I am speaking about them in the present perfect. I’d be saying that I might have more of an impact (in the future) than my brothers have had (so far). That’s the same mistake we’d be making if we chose C or E on this problem. We don't want to say that the principles could (in the future) have more significance than the particulars have (up to now).

Hopefully now, those with concerns can see why D works. The word “do” is actually filling in for the verb phrase “have significance.”

By the way, we need “do”--rather than nothing--to avoid ambiguity. A & B pose this problem in different ways.

B: “The guiding principles of the tax plan released by the Treasury Department could have a significance that is even greater for the economy than the particulars of the plan.” There are a few ways to read this sentence (and that's the problem), but to me it seems like we’re saying that the significance of the principles could be better for the economy than the particulars are. We should be saying that the principles are more significant (or “greater in significance”) than the particulars.

In A, we have two problems. First, the word order is wrong—“could have even a greater” just doesn’t work, because “even” seems to be modifying the verb “have” instead of the adjective “greater,” as it should. Second, without our helper “do,” we still have some ambiguity. A could be read as “The guiding principles of the tax plan released by the Treasury Department could have an even greater significance for the economy than FOR the particulars of the plan.” In other words, without a clarifying word (either the “for” that I just added, or the “do” that we add in D), we aren’t sure which interpretation to go with.

I hope this helps! Let me know if I can clarify anything.