"We've got to come out of it united, with a strong focus on what we can do for New Zealand."
McKelvie said MPs had not met face to face for a while but there had been a lot of phonecalls going around the caucus, in the lead-up to the leadership challenge.
Muller is in his second term in Parliament and is National's agriculture spokesman.
Bridges is the MP for Tauranga and in his fourth term in Parliament. He became National's leader after Bill English stepped down in February 2018.
McKelvie said Bridges had had a tough eight weeks with Prime Minister Jacinda Ardern "very prominently out there" during the Covid-19 response.
"It's very difficult for someone leading a political party in opposition anywhere in the world," he said.
For Whanganui MP Chester Borrows said there were no rules for how a leadership struggle is conducted - except that the challenger had to nominate themselves.
After that someone will make phonecalls and "do the numbers" - get the names of their supporters. People who are undecided may get calls from all the parties in contention.
Borrows is guessing that Bridges will not step aside.
"Simon Bridges is a bit of a scrapper, and I doubt if he is going to make too many concessions," Borrows said. "I'm assuming it will probably come down to a vote."
Loyalties on the day are remembered, Borrows said, and those who vote against the leader may be "cast into the outer darkness" for some time.
What's intriguing Borrows about this contest is that Judith Collins, the National Party "elder statesman" most often mentioned in preferred prime minister polls, is not taking part.
"She always plays a very close game."
He's guessing Collins thinks she will have a better chance at leadership next election.
Current Whanganui MP Harete Hipango was contacted for comment.