Australia will know its new deputy prime minister on Monday morning, with Michael McCormack, the veterans affairs minister, expected to be appointed the new Nationals leader to replace Barnaby Joyce.

The Nationals will meet in Canberra at 8am on Monday to select a new leader after Joyce last week confirmed he would go to the backbench after a fortnight of ceaseless controversy about his private life, and the lodgement of a sexual harassment claim against him with the National party, which he contests.

The New South Wales MP David Gillespie withdrew from the race on Sunday afternoon. There had been speculation that agriculture minister and staunch Joyce supporter, David Littleproud, could have a tilt but late on Sunday he said he would not stand.

The Nationals deputy leader, Bridget McKenzie, signalled it would be desirable if only one leadership contender put up their hand on Monday morning, and she said the Coalition agreement did not need renegotiation.

McKenzie told the ABC on Sunday it was important the government, which has been battered by the controversy, achieved “a seamless transition tomorrow”, rolling over the existing private agreement between the Liberal and National parties, and ministerial portfolios, rather than putting everything up for grabs.

She said “conventionally” the leadership of the National party had been decided by acclamation rather than a contested process. That had always been the situation in the past, McKenzie said.

When asked whether the Coalition agreement should be made public, McKenzie said the document was administrative, not “sacred” and she said: “The governor general is across it. That’s all that we need to worry about.”

With the Joyce imbroglio dominating political coverage for the best part of a fortnight, a new ReachTel poll commissioned by Sky News had Labor ahead of the government on a two-party-preferred basis 54% to 46%.

Over the weekend, the outspoken Queenslander George Christensen declared the Nationals should use Joyce’s departure as a trigger to end the formal coalition with the Liberals.

Christensen said on Facebook he would “rather see a Liberal prime minister, Liberal deputy prime minister, and a full cabinet of Liberal ministers than have to compromise our values and the welfare of the good people we represent”.

“We should not let the trappings of politics and positions of power compromise our desire and our ability to deliver,” he said.

Christensen’s NSW Nationals colleague, John “Wacka” Williams, flatly rebuffed that idea. “George can have his opinion but we’d lose so much – we’d lose our ministers who deliver the achievements for regional Australia.”

Over the weekend in Washington, Malcolm Turnbull – who publicly excoriated Joyce for his conduct before leaving the country – papered over the row by declaring the Coalition would remain “strong and enduring”.

The education minister, Liberal Simon Birmingham said on Sunday “George says a lot of things” but he said the Nationals as a group understood that the best way to influence anything was “to be at the table”.

In South Australia, the deputy Liberal leader, Julie Bishop, said come Monday morning there would be a new leader of the National party “and the Coalition continues”.

After Joyce confirmed his intentions last Friday, McCormack positioned himself as the unity candidate.

While some colleagues are concerned he won’t stand up against the Liberals in the way that Joyce did, McCormack has declared himself a “fighter” with “the drive to deliver”.

“When water rights were challenged in my electorate, I crossed the floor to get a better deal. When a big American company came knocking to take over GrainCorp, I stood up for our farmers and opposed it,” McCormack said in a statement after Joyce’s resignation.

• with Australian Associated Press