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While Muller is yet to make any public statement at all about his bid, Bridges seemed to remain confident this afternoon.
MPs have been summonsed back to Wellington in a recess week after Bridges called an emergency caucus at midday Friday to settle the matter.
All eyes will be on the 1News-Colmar Brunton poll at 6pm tonight as those MPs decide whether to back Bridges or take on challenger Todd Muller just four months before an election.
Bridges seemed confident ahead of that vote, quipping on a Tourism Industry Association conference zoom today that "sad for you, I think you'll still be seeing a lot of me" after TIA head Chris Roberts acknowledged that vote.
Despite that confidence, many MPs are staying quiet about who they are backing, and one said he expected it to be "very, very close".
Tonight's poll may be the deciding factor for MPs who are still teetering after the dire 30.6% in Monday's Reid Research poll.
The 1 News poll was taken a week later than the Reid Research poll, and began the day after the Budget was delivered and ended on Wednesday night.
That means it will take in the period of leadership turbulence within National - a factor which is unlikely to help the party's result.
Both contenders were spending the day calling around their fellow MPs to either shore up their support, convince undecided MPs to back them, or poach those from the other side.
The vote will take place at a midday emergency caucus meeting. It is a secret ballot, and most MPs were keeping their choices to themselves.
Muller arrived in Wellington on Thursday morning, but has not yet made any public comment about his challenge. It was announced by way of an email to MPs, which was swiftly leaked to the media.
He was spending much of the day away from Parliament on the phone trying to secure the support to get his bid over the line.
His running mate Nikki Kaye also had little to say today - both sticking to the line that it was now for the National Party caucus to decide on the leadership.
Simon Bridges was also still rallying his numbers and cancelled all his media interviews for the day.
However, he continued to chair the Epidemic Response Committee for part of the morning and to address the Tourism Industry Association conference.
In that he apologised for the absence of his Tourism spokesman Todd McClay, saying McClay was on a plane from Rotorua heading to Wellington for tomorrow's vote.
McClay is a Bridges supporter, and Bridges quipped he was very keen for McClay to make it to that vote.
Bridges' wife Natalie has also now come to Wellington to support him.
MPs working for each side ruled out any chance that the matter could be settled ahead of the vote, indicating there is no landslide of support either way. One MP said he believed it was "very close".
Most MPs the Herald spoke to said they did not wish to disclose their positions out of respect for the process of caucus.
Of those that are known, Muller's core support base includes Chris Bishop, Amy Adams, and Nicola Willis as well as Kaye.
Bridges' core support base consists of his deputy Paula Bennett, Michael Woodhouse, Todd McClay and Paul Goldsmith. MP Brett Hudson has publicly backed Bridges.
Bridges is also understood to have Mark Mitchell's support. Mitchell would not comment, saying he wanted to respect the caucus process.
Mitchell had previously put his name up for the leadership himself in 2018 after Bill English stood down, but withdrew before it went to the vote.
Mitchell's vote and that of Judith Collins could be critical if their decision also tips the votes of their own supporters the same way.
That may rely on the positions that are offered up in return for support.
Collins has refused to say who she will support, and said any discussions with the two candidates were confidential.
On Wednesday, she ruled out contesting it herself, saying she knew a messy leadership change before an election would damage the party.