Since this is a non-binding vote feel free to call it whatever you'd like. There were so many good options that it would be a shame to call it just one thing. A few more have trickled in...
The Bible Told Me NOT To Amendment
The Wrong-wing Procreation Nation Amendment: If you can't procreate, you can't mate.
The Pandora's Box Amendment
The Read it ALL Before You Vote Amendment
The Unintended Consequences Amendment
The Let the Government into Our Homes and Private Lives Amendment
We Hope You Don't Read the Second Paragraph Amendment
The no man +óGé¼+ôShallmar/Newman+óGé¼-¥ amendment
Gay Bashing Amendment
Check this previous post for many more options
On a more encouraging note, it certainly appears that this amendment can be defeated when looking at more than just the headline (i.e. first paragraph). As noted by RK posters and readers (and elsewhere), when other aspects of the amendment are brought into play the support for the amendment drops.
This is further bolstered by the recent PEW poll on social issues which discusses, among other things, the public's attitude toward homosexual relationships. Hat tip to PM for bringing it up. While there is still strong opposition to gay marriage (56-35), civil unions are actually favored (54-42).
Because of this the amendment is vulnerable. Not only does the wording deny homosexual civil union, it also doesn't allow heterosexual civil union. If there is moderate support to allow homosexual unions then there should be overwhelming support to allow heterosexual civil unions. I'm not sure if there have been many opinion polls regarding heterosexual civil unions, but it's hard to imagine that support wouldn't be a lot higher.
Heterosexual civil unions are probably not on the agenda for most because those straight folks can just get married. The fact that the amendment, while targeting homosexuals, will severely restrict everyone's civil rights should upset the majority regardless of their feelings on homosexual unions.
If the public becomes aware that this restrictive amendment will affect heterosexuals couples as well as homosexual couples, it's introduction could have exactly the opposite effect that it's sponsors intended - many people will come out in opposition who might not normally vote. And so the challenge becomes how to effectively promote the anti-heterosexual aspects of the amendment.
I hope it helps defeat this horrific attempt to turn George Mason's historic Virginia Bill of Rights into a Bill of Rights Plus One Wrong.