As the Mechanical snail points out, this has now been implemented, though not quite as-requested.
Of note:
Only accessible from the review queue (so rather difficult to target a specific question). Yes, this is very much by-design.
Voting against closing does not override anyone's close vote. However, a sufficient number of "Do Not Close" responses (currently 3) will kick the question out of the review queue and start aging the close votes - regardless of how many views the question has had.
If the question is closed, Do Not Close votes do not translate into re-open votes. However, we may use them to prioritize items in the Reopen Queue.
The philosophy behind this is reflected in my response to Miles' bounty:
The development of new Stack Exchange sites has led to a disturbing tendency for on-topic questions to attract close/migration votes from a minority of users simply because they are arguably "more on topic" at a different Stack Exchange site. The "silent majority" cannot prevent such migrations. The suggested (and notably unpopular) approach of monitoring questions until they are closed, and then voting to reopen, does not work in migration scenarios. Let's revisit this feature request.
When you find a problem with the way in which folks are behaving on the site, try to correct it with a scalpel, not an axe. The "silent majority" can prevent such migrations:
If you see a question being closed that shouldn't be, leave a comment expressing your rationale. Make it constructive - "I like this question, therefore it should stay, close-voters are stupid" accomplishes little.
If you see a good, on-topic question in danger of being migrated, flag it - a moderator can always step in to prevent the migration. Note that we can and do review migration paths available to ordinary voters to address problems with migrations.
Answer the question. Most of the sites on Stack Exchange are not available as migration targets for non-moderators. Moderators are encouraged to decline flags asking for clearly on-topic questions to be migratedModerators are encouraged to decline flags asking for clearly on-topic questions to be migrated. And nothing says "this question is on-topic" quite like a good on-topic answer.
We're also working on revamping the "review" tools to put questions on the path to being closed in front of those with the most expertise in their topics. I can't always tell if, say, an r question is better off on Cross Validated, but there are plenty of folks who can. This will also give us some better data for determining when the silent majority has actually reviewed a question, and the ability to then age close votes accordingly. Which is really what you want.
Requiring that "silent majority" to go around casting "unclose" votes wouldn't do anything but create more work within the system for the benefit of a few edge-cases and a rather larger increase in the ability for griefers to waste the time of those already going out of their way to review and moderate. It's a tool for creating gridlock, something Stack Overflow in particular doesn't need any more of.