Swarbrick said the numbers were "looking promising" and she would work hard in the following 24 hours to try to get her bill over the line.
"I'm disappointed in the National Party position. It is a conscience vote at the end of the day.
"I do hope that it weighs on their conscience. They are going to making this vote in front of those patients who would benefit from its use.
"This isn't about MPs in the house. This is about New Zealanders who are currently suffering who would benefit from the use of medicinal cannabis."
Swarbrick said the bill wasn't perfect, and misconception about the growing aspect of her bill was putting some people off. But she remained hopeful that the issue could be sent to select committee.
NZ First leader Winston Peters said he would vote against Swarbrick's bill, but it would be a conscience issue for the rest of caucus.
While most Labour MPs intend to support it, it is understood Swarbrick is about 10 votes short of getting it through to select committee.
Swarbrick's bill will allow the terminally ill and those suffering chronic pain to use and grow marijuana for medical use – but some have concerns about its breadth.
National's health spokesman Jonathan Coleman said it was a "loose bill".
"Effectively if they want to decriminalise cannabis they should just bring that to Parliament.
"You have a bill where anyone, on a doctor's say so, can cultivate cannabis or have a relative or designated person do that. That's a pretty broad scope."
He was concerned it would mean pressure on doctors to sign off on it.
Prime Minister Jacinda Ardern is among those supporting it, saying she wants a debate on whether the law should be more liberal than a Government bill will achieve.
A Government bill which provides for people with terminal illness to have a legal defence for using medicinal cannabis will go before Parliament on Tuesday and Swarbrick's more liberal bill will be debated on Wednesday.
Ardern said the Government bill was an improvement on the current position but many would have liked it to go further.
"Chloe Swarbrick's bill is an opportunity for those people of that view to have that debate. I want that debate to happen in this Parliament so I will be supporting it to select committee."
The Government bill was a compromise to ensure it had NZ First support to pass.
"The Government bill forms a consensus across three parties as to how far they are content to go and we can guarantee the numbers for that bill.
"Chloe Swarbrick's goes a step further and we want to test whether there's an appetite in Parliament to do that."
Swarbrick's bill would allow those with terminal illness or in chronic pain to use – and grow – cannabis for medicinal use.
It has the backing of former Prime Minister Helen Clark who tweeted in support of it earlier this week.
Clark was recently appointed to the Global Commission on Drug Policy, a prominent drug reform panel.
National and NZ First were due to discuss Swarbrick's bill in caucus meetings on Tuesday morning.
National MPs were not saying which way they would vote prior to caucus.
It will be a conscience issue for the Labour caucus.
Finance Minister Grant Robertson also said he would support Swarbrick's bill, saying the issue needed to be considered in the broadest terms possible.
"My personal view is that medicinal cannabis has got an important role to play in supporting people who are in chronic pain and who are terminally ill."
Transport Minister Phil Twyford was also a supporter. "My middle name is Stoner. So that's a yes."
