Treaty really doesn't matter without Senate ratification and then it won't matter much as the courts have already ruled that treaties can't usurp the Constitution.
Having said that, no amount of signatures on a petition will matter much to Obama. Remember, this is a guy who lied and tried to say that 90% or close of NRA members wanted more gun control, then had a fit when the Senate did not pass his bill. This is the same guy who forced Obamacare through using reconciliation because it would not pass a straight vote. He did this when close to 90% of Americans didn't and still don't want it.
This guy is going to do whatever he wants, regardless of what we want or what the law is.