One vote. That's all the flag-burning amendment needs to become law.
It currently has 66 supporters in the Senate (it needs 67). It's passed the House. It will be ratified by all 50 state legislatures (more than the 38 needed) if it gets through the Senate.
Fans of the flag-burning amendment like to bring up how many soldiers have died for that flag. Actually, I thought the soldiers died to protect their countrymen's freedom. Which includes the freedom to do things like, oh, say, burn the flag. Oh, and when the President takes the oath of office, does he talk about preserving, protecting, and defending the flag? No. He swears to preserve, protect, and defend the Constitution.
Sure, flag burning is despicable. But just because an action is despicable doesn't mean we should outlaw it. We can't differentiate between speech we like and speech we don't like - otherwise "freedom of speech" becomes meaningless. Any constitutional amendment that cuts into the First Amendment rights that make our country special is not a monument to those who died for this nation - it is the worst possible affront to their memories.
Update: Bob Kerrey agrees with me.