Nash said while the polls would be discussed, he did not expect a confidence vote on Little's leadership.
"And if there is, I will speak very strongly in his favour. Of course people are concerned about the result, you'd be lying if you weren't. But he has my support 100 per cent."
He did not believe there was an appetite to change leader two months before the election.
"I think a change in leader would doom us. Absolutely doom us. In fact, it could put the party itself in jeopardy."
Nash said he was not one of the colleagues Little had spoken to about stepping down but was not surprised Little raised it. "I'm not because he's a man of integrity and when a poll like that does come in it's a bit of a shock and he needed to seek a mandate from his close advisors and it sounds like he's got one."
He was "a little surprised" Little had spoken publicly about stepping down. "But he was going to be asked about it anyway, so he's front-footed it."
Little's deputy Jacinda Ardern - who is considered most likely to replace Little if he did step down - said she was one of the colleagues Little had discussed the polling with.
"I confirmed I supported him. I've made it very clear that Andrew has my support."
She said nobody was happy about the polls. "We know that we need to do better. I think what people want to hear from us is less talk about us and more talk about issues."
Front bencher Phil Twyford also said Little had his support.
""I support the leader of the Labour Party as long as he is the leader of the Labour Party." He said nobody was satisfied with the poll numbers.
"We don't want to be in this situation. We want to be in a much stronger position to form a Government.
But the responsibility to deliver messages and explain our policies is not just Andrew's. It falls on all of us so it is a collective responsibility."
Nash said he believed the polls would improve once the campaign proper started and voters starting looking at their options. "At the moment all we are hearing about is Todd Barclay, and Metiria Turei. Those aren't the issues important to New Zealanders."
Another MP Kelvin Davis said he also backed Little and hoped the polls would level out once the attention stopped going onto Turei.
However, Labour MPs relying on the list may be less optimistic if the polling means they will be cut out of Parliament.
That includes David Parker and Trevor Mallard, as well as Little himself who might not return if Labour drops further.
The poll results have disappointed the party after unveiling a major package of reforms including boosts to Working for Families and new payments for parents of newborn babies - although it is also scrapping National's income tax cuts.
Labour is putting the results down to the attention that has gone on Green co-leader Metiria Turei's admission of welfare fraud when she was a solo mother - something Little pointed to in his speech to the party's Maori candidates on Sunday as dominating media coverage.