Cabinet rejected passing a "self-executing" bill into law that would be enacted in the event of a "yes" vote, which was the preferred option of the Green Party and Paula Bennett.
The paper said this option would have given "maximum certainty about what would happen, and when, immediately following the referendum".
Neither Little nor Prime Minister Jacinda Ardern would not say whether Labour would have preferred a self-executing bill.
Asked if New Zealand First had blocked this option, Little said: "No, you're completely wrong. Actually, like all these things ... we negotiated our way through it."
Little said passing a bill into law and having it enacted in the event of a "yes" vote was "pretty much the same" as having a draft bill in place.
He said it would still be a binding referendum because Labour, New Zealand First and the Greens have agreed to pass the bill into law if there was majority support in the referendum.
He asked National to make the same pledge, but Bridges said he would not without first seeing the draft bill.
"I would need to have answers to some basic questions like: What's the tax rate going to be? Will gangs be able legally to sell drugs? Will edible gummy bears be legal?" Bridges said.
"Laws as they start in Parliament are not the laws that finish. There's just no certainty. There's no binding referendum here."
Bennett said having self-executing legislation was the only way to make the referendum binding.
"Let's make it really clear: this is not binding. He [Little] cannot spin it that this is binding purely because him and the Greens might say they're going to agree to it.
"It is shame that a select committee, with its experts and public submissions, do not get the opportunity [before the referendum] to get into the detail of things that might sound good in principle, but when you get into the detail are very complex."
Green Party spokeswoman for drug law reform Chloe Swarbrick said the announcement delivered on the Labour-Green confidence and supply agreement, which committed to holding "a referendum on legalising the personal use of cannabis".
She described the process as binding, adding that "no parliament can bind future parliaments".
Bennett has previously declined Swarbrick's invitation to join a cross-party group on drug law reform, but was open to being part of the cross-party group agreed to by Cabinet yesterday that would allow National to have input into the process.
"Sure, if its headed by a minister," Bennett said.
"I just don't see how, with all respect, a junior MP who is not part of the Government is the spokesperson on drug reform that could change the social fabric of this country."
