The young people are hoping it gets cross-party support and said a change to policy will count for more than the actions of individuals.
Climate change is something their generation has to lead, they said, and it affects everybody.
"We can achieve a zero-carbon economy and adapt to climate change - it's whether we have the will to do it," Mr Young-Drew said.
The riders are using the Tour Aotearoa cycle route, which is mostly off main roads. They include cities where they can, and on Tuesday talked to children at St John's Hill School and to Whanganui Mayor Hamish McDouall.
He told them he would announce his personal endorsement of the Zero Carbon Act within 48 hours.
The five have been joined by others, and hope to have a big crowd as they bike from Lower Hutt to Parliament on Thursday.
Before arriving in Whanganui they took the Mountains to Sea cycleway and Whanganui River Rd, and they spent Monday night at the Quaker Settlement. They have suffered sore muscles and eaten "compost wraps" (last night's dinner in a wrap) along the way.
But Mr Young-Drew is buoyed up by conversations he's been having.
"I haven't met a single person who seems resistant to the need for change to combat climate change," he said.
Generation Zero has about 100 active members and 25,000 supporters. Members meet by Skype and use social media to spread their message. Their online petition at www.zerocarbonact.nz has nearly 13,000 signatures.