The work was shared and they both signed it. Bush spearheaded and promoted it and he signed a ceremonial first draft which still required ratification by the US Senate. He tried to fast track the approval but failed and had to leave it to Clinton when he lost the election. Clinton added two side agreements, The North American Agreement on Labor Cooperation (NAALC) and the North American Agreement on Environmental Cooperation (NAAEC). They are meant to prevent failure of enforcing labor and environmental laws in the member states. This was the version that was then sent to the Senate and signed into law.

I think who gets the credit and whether the credit is actually blame probably depends a lot on the political affiliations of the one who is talking about it. It was a cooperation between both parties though, Republicans and Democrats both agreed with it at the time though apparently there was more discord among Democrats. In Senate it was 27 democratic votes and 34 republican votes yea and 28 democratic votes and 10 republican votes nay.