Bridges' position is under scrutiny after a political poll showed support for National had plunged.
He told RNZ's Morning Report programme today that he and deputy Paula Bennett are being both being challenged, and he was confident he had the support of the majority of caucus.
He would not say who the two challengers were. The New Zealand Herald is reporting the two challengers are understood to be Todd Muller and Nikki Kaye.
The leadership vote is likely to be at a caucus meeting next Tuesday.
The latest Newshub Reid-Research political poll has National with just 30.6% support, and in the preferred Prime Minister's stakes Bridges is on 4.5%.
At the same time Labour and Jacinda Ardern are enjoying a huge surge in popularity.
Former National MP Bob 'The Builder' Clarkson, who used to hold Bridges' Tauranga seat, is still backing the leader.
"He's well educated, he doesn't swear like me. So I think he's a decent sort of guy, actually," he said.
"He might not pick the right subjects to talk about sometimes but generally I think he's a nice guy. He's a family man and everything.
"But the leader of the Labour Party has had a charmed run as a politician - she's on the TV 90 percent of the damn time, and that's hard to beat."
Some voters in Bridges' home suburb of Matua concede National's leader has made mistakes but, for the most part, they're forgiving.
"Aside from what I believe was a mistake very early on in the pandemic when it became a little political, I think he's done very well," said one man.
"I guess a lot of the things that the government's done and proposed probably aren't too dissimilar to what National would have done. He just really hasn't done a very good job of - if there's an alternative - getting that across," said another.
One Tauranga voter said he could come across as "a bit bombastic".
"Oh my goodness, just speak to someone - you're not speaking at someone all the time and always having to get your point across. He doesn't seem to listen very well," she said.
"I don't always like what Jacinda Ardern does, but because she comes across as genuine I think that's what makes her the winner."
In the safe National seat of North Shore, it was hard to find anyone with a positive thing to say about Bridges.
"I'm a long-standing National voter and I wouldn't vote for him. I like the ol' Crusher," said Marjory, with a laugh, referring to National MP Judith Collins' nickname.
Peter Bedford said one of Bridges' problems was that he wasn't memorable.
"Three of us were talking the other day and none of us could remember his first name, which is quite brutal."
Bobby Barker from Devonport said Bridges seemed to like being the contrarian.
"I think he doesn't really have any opinions of his own - his opinion is whatever is the dissenting opinion. I don't think he's once come across as honest or anything, just disingenuous."
Rose Hunt from Takapuna said she "just can't listen to him".
"Simon Bridges, he needs to go. He needs to go - a bit like Donald Trump needs to go."
The National Party caucus is now anxiously awaiting a fresh poll later this week.
At the party caucus next Tuesday, MP's are likely to decide whether or not to topple their leader.
Former National Prime Minister Jim Bolger is promoting Bay of Plenty MP Todd Muller.
"Todd has the ability to work well with all across world, across the line. He's not that harsh partisan position, he will work with others to achieve the right goal," he said.
Simon Bridges and his party are now faced with crucial decisions three months out from the general election.
