In an interview with the FT Weekend magazine, she said they would not vote for a “flimsy bit of paper” simply because the Government said the alternative was no deal.
A Labour source said the party’s position had not changed and Ms Thornberry was simply being “sceptical” about the prospects of the Government reaching an acceptable agreement.
Nevertheless her comments add to the pressure on Mrs May who is facing strong opposition to her Chequers blueprint for leaving the EU from hardline Tory Brexiteers.
Without support from at least some opposition MPs, the Government may struggle to get any agreement through Parliament.
Downing Street is hoping the prospect of a no-deal Brexit will force critics to fall in line.
However, Ms Thornberry warned ministers appeared to be heading to a defeat, paving the way for a general election.
She said: “I can’t see them coming back with a deal that is going to meet our six tests and I can’t see them coming back with a deal that will unite the Tory party, for heaven’s sake.
“They are not capable of governing… a general election in the autumn or we’re going to have it in the spring.” Her comments will come as a setback to Labour pro-EU campaigners who want the party to back a second referendum.
Ms Thornberry said the Chequers plan, which would see Britain have a “common rulebook” with the EU for trade in goods and agriculture, was too vague to work.
She said: “I don’t think this kind of half-in, half-out of the customs union will work. It’s just full of red tape and going to cost us too much money. It’s just nonsense.”
Meanwhile, arch-Remainer Gina Miller yesterday launched a national campaign to derail Brexit.
The Guyana-born former model wants to “end the chaos” of Brexit by publishing “unspun facts” so people can decide themselves what they want to happen next.