Actually, the treaty was signed by Pres. George Bush, the first--a Republican. It was not ratified by the U.S. Senate until after Clinton took office--ratified by a REPUBLICAN controlled U.S. Senate. N.A.F.T.A is a treaty, not a law. Since it is a treaty, there was no need for President Clinton to sign it. It had already been signed by President Bush. It only needed ratification by the U.S. Senate.
Actually, the Senate was controlled by Democrats late in 1993 by a margin of 57-43 as a result of the 1992 elections. Nevertheless, 27 Democrats in the Senate voted in favor of NAFTA, joining 34 Republicans.