The offer, announced on Monday, runs until the end of October. It included two long weekends - Queen's Birthday and Labour weekend - and two school holidays.
Bookings for the school holidays were starting to fill up, Webster said.
Most of the bookings were from Auckland and demand was strong for larger campervans, but the Queenstown and Christchurch operations had also sold out for Queen's Birthday weekend.
Webster said the huge, and unexpectedly strong, response wouldn't help the international tourism company's damaged balance sheet but would save some staff jobs.
The company had pulled in its Australian staff and "everyone in the business" to handle the response, with more than 50 people on the phones at any one time.
He said the Tourism Holdings website was only built to handle a certain amount of traffic and "no-one" could have anticipated how massive the response would be within two days of the offer opening, he said.
"I have mixed feelings - I'm really pleased New Zealanders are taking the opportunity of getting out, but I'm gutted about the number of people that haven't been able to get through yet.
"Give it a bit of space - we will get back to you."
Bookings need to be made in the next eight weeks.
The company said the initiative was to enable Kiwis to have a well-deserved holiday and support regional communities and small businesses feeling the pain of reduced visits from international visitors and local travellers.
"The Great New Zealand Road Trip" was on the bucket list of many Kiwis and the offer went a way to making it a reality, Webster said when launching it on Monday.
The offer represents a 35-40 per cent discount on usual winter campervan rates and a 65-70 per cent decrease on September school holiday to October end rates. Rates range from $29-$69 a day and vehicles can be booked now with a $1 deposit.
A trip over a long weekend at $29 a day would cost from $87.
"This is for the community, saving jobs and giving Kiwis this once-in-a-lifetime experience," Webster said.
"We are losing money anyway - this isn't about money-making, it's about helping the New Zealand economy. We are an international tourism business and there is no international tourism. After weeks of lockdown, many Kiwis have expressed interest in domestic travel."
In looking at what costs inhibited Kiwis from doing road trips, the company identified one as the cost of kennels and catteries for their pets, he said.
So it decided for the first time ever to let pets on board for a $100 cleaning fee, no matter how long the hire. Bike racks can be added for a fee.
The number of pets allowed on one vehicle is at the company's discretion, but Webster said generally the maximum would be two.
Insurance cost cover, or liability excess, as it's called has been cut from up to $49 a day to $10.
The company is also offering discounts at its cave tourism hotspot the Waitomo Group of visitor attractions.
Minimum hire of the company's Britz and Maui campervans has been reduced to three days from the normal five, and cancellation fees don't start until seven days out - usually it's 90 days. The special offers are until July 19.
The company is open seven days in Auckland, Christchurch and Queenstown. It is offering late night branch hours on Fridays for after-work pickups.
Tourism Holdings is the world's largest operator of recreational vehicle rentals, with signature brands in New Zealand, Australia, the USA, and UK.
In New Zealand, the majority of its motorhomes are manufactured locally by joint-venture Action Manufacturing.
The company is also the largest national seller of motorhomes to private owners. It operates the award-winning Kiwi Experience bus service, Waitomo Glowworm Caves, and Black Water Rafting.
