It is already "possible" to do this!

Step 1

Go to the new Review interface for close votes.

Step 2

Click through the ≈ 60,100 questions (on SO) with close votes until you see the one you want to vote not to close.

Step 3

Click Do Not Close.

Step 4

Profit!

And...problem solved!

But seriously

The functionality already exists, but is hard to use. If you agree with a close vote, you can always cast your vote to close directly from the question. Why should it be harder if you disagree?

(Also, it seems the queue interface is biased toward more recent questions, so you wouldn't have to click that many times. And voting not to close doesn't literally cancel out a close vote, but if several people do it the question is removed from the queue.)

More discussion

Shog pointed out that close votes come with reasons to close, and so contain more useful information. (Here we're not concerned about obvious duplicates and the like; people aren't going to be disputing those: only the more complex cases.) Shog is afraid that allowing no-close votes will lead to people canceling out close votes without providing a useful rationale. I'll grant you that's a problem, but the problem is symmetric: close vote reasons are vague and often require additional explanation for why they apply, and most of the time close voters don't explain exactly why they think it's e.g. a duplicate. Fundamentally it would be no harder to comment along with your no-close vote from a question, than to add a useful argument along with a your close vote for a non-clear-cut question. I therefore see the no-close-vote proposal as orthogonal to the problem of people not providing rationales.

For example, I have seen a fair number of duplicate votes for which the questions look subtly different; it may require a minute or two of reading to determine whether they really are dupes. In these I don't recall ever seeing comments like "This poster's underlying problem is xxx which is the same as the other question".

Because it's easier to get questions that should be closed out of the queue, the current system encourages questions getting closed and reopened repeatedly. Lack of explanation is a different problem; perhaps adding a comment field to the (no-)close dialog would help.