Ms Steinke's parents, Geraldine and James, have flown from Colorado to be by their daughter's bedside. They met Mr Stithem's family in Los Angeles en route to New Zealand.
Friends and family in the US are in shock over the accident, which happened just six days after the Denver-based couple married.
A Facebook page has been set up to offer support and share information.
Wedding guest Irene Sisneros wrote that she would always remember the way Mr Stithem looked at his bride throughout the ceremony.
"There was nothing but complete and absolute love and adoration. I do believe that he will continue to look this way at his sweet Kirsten, only now he has angels by his side looking with him."
Another friend, Rachel Clement, said: "This is what keeps breaking me to pieces. He loved her so much, and she him."
Ms Steinke, aged 28, is a communications manager at the University of Colorado and has worked there for about five years.
Colleague Karina Colvin told the Weekend Herald staff were hoping for good news.
"Our hearts are crushed here. I just can't believe how tragic this whole situation is. I just saw Kirsten the day before she left the office to have her wedding and here we are ..."
Ms Colvin said the couple were "absolutely amazing".
Jason Medrano, who had been mates with Mr Stithem for 20 years, wrote that he would miss his childhood friend and the memories they shared. Mr Stithem worked as a property consultant.
Meanwhile, the public is calling for improvements to be carried out urgently at the intersection of SH3 and Waitomo Caves Rd, which has been the scene of two fatal crashes this year, both involving tourists.
The New Zealand Transport Agency plans to carry out more upgrades and is considering signage options to alert motorists and warn them of the intersection ahead.
Several readers have suggested signs saying "Crash Zone" be installed to warn tourists.
