"The main impact is on TTIP (transatlantic trade investment and partnership)," Andre Sapir, a senior fellow at the Brussels-based think tank Bruegel, told CNBC over the phone.
Sapir explained that there are three possible outcomes: CETA goes through with some modifications, meaning it will be fully approved but at a later stage; CETA goes through but without some of the parts that are deemed more sensitive; or "the least probable scenario" that the whole agreement is scrapped.
The first case would be "good news", because the EU would still be able to take CETA as a template in the current trade negotiations with the U.S., and without being forced to make concessions. The other two options would damage the EU's reputation as a trade partner even further and weakening its negotiating power.
TTIP, which began to be negotiated in 2013, is far from reaching initial hopes that a "skeleton" of an agreement would be done before U.S. President Barack Obama leaves office at the end of 2016.
Meanwhile, Chystia Freeland, the Canadian minister for trade, said last week that the EU was "not capable" of signing a trade deal and that her country was "disappointed."
"It seems evident for me and for Canada that the European Union is not now capable of having an international accord even with a country that has values as European as Canada," Freeland said.