The problem is, under the US Constitution, the President does not have authority to sign any treaties until first ratified by 2/3 of the Senate. And with the current members of the Senate, such a treaty will never get anywhere close to a 67/23 vote. Or, not in favor of it anyway. The Senate recognizes that their constituents are so firmly against such a thing that they will never approve it, and even if ALL the Democrats did vote for it (which they won't; the "blue dog" Democrats won't vote for it), there are enough Republicans (even after discounting the RINOs ["Republican In Name Only]) to ensure any such UN treaty to ensure a firm rejection.
Without this authority, the President is undermining the government and meeting the very definition of treason.