Two Labor rightwingers, Chris Bowen and Jim Chalmers, are weighing up whether to run for Labor leader against Anthony Albanese, effectively forcing the party to undertake a grassroots ballot.

Bowen, Labor’s most senior rightwing figure, has lost bark in the caucus because of his championing of controversial revenue raising policies, particularly franking credits, which hurt MPs in marginal seats – and Chalmers, a next-generation rightwinger from Queensland, is being lobbied to run to help stabilise the ALP’s position in a state where voters swung to the Coalition and to insurgents.

Chalmers will be influenced by Bowen’s decision, which is expected on Tuesday. Backers of Albanese would welcome a full-blown leadership ballot, confident the high-profile leftwinger would prevail both in the grassroots vote and in the caucus. A number of Labor players are in the mix for deputy leader, including Tony Burke, and Victorians Clare O’Neil and Richard Marles.

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Tanya Plibersek, who had been preparing to run against Albanese, removed herself from contention on Monday. The jockeying within Labor – which includes a significant recalibration on tax and climate policy – came as the election count on Monday shored up the Coalition’s numbers in the parliament, with Scott Morrison now expected to govern in majority.

Morrison convened a meeting of his leadership team and the national security committee of cabinet on Monday.

The prime minister says the first order of business for the Coalition will be to legislate tax cuts, which may require the recalling of parliament before 1 July when they are due to come into effect. He will also embark on a reshuffle of his frontbench, with several key positions up for grabs.

Conservatives in New South Wales will be angling for better representation as a unifying gesture in the wake of Tony Abbott’s departure from politics, and Arthur Sinodinos, who has battled cancer, has signalled his interest in returning to the cabinet, noting he had returned to political life because he was “keen to contribute”.

The attorney general, Christian Porter, has been appointed manager of government business in the House of Representatives, replacing Christopher Pyne.

On Monday night, the home affairs minister, Peter Dutton, told the ABC he would not have held his seat of Dickson on Saturday night had Malcolm Turnbull remained prime minister, and predicted Morrison would remain consultative with colleagues despite securing victory with a presidential campaign.

Dutton said Morrison had consulted daily with the leadership group throughout the campaign, “and we talked through issues, we talked through what our problems were, where the opportunities were, threats – all of that”.

He said the Coalition hung on to government because voters in Queensland, the regions and the outer suburbs were suspicious of Bill Shorten.

With the Australian Electoral Commission prioritising the count in close seats on Monday, the Liberal party inched ahead in the eastern suburbs seat of Chisholm, a likely victory which will bring the Coalition’s numbers in the House of Representatives to 77.

The Coalition has also won back Turnbull’s old seat of Wentworth from independent candidate Kerryn Phelps, electing Dave Sharma to the seat.

Phelps said that while she believed people in the wealthy Sydney electorate wanted a socially progressive local member, the electorate was more concerned about a prospective Labor government.

“There were people who were appreciative of the work that I had done, but they didn’t want a Labor government in this area, so there was this conflict,” Phelps said.

“There were people who are still upset about Malcolm Turnbull being removed, but others who felt more strongly that they preferred a Liberal government. There were complex issues involved but in the end it was a line-ball decision and it fell to the Liberals.”

The Coalition has committed to repealing the medical evacuation legislation spearheaded by Phelps in her brief time in Parliament.

Three other Labor held seats remain in doubt, including Macquarie in New South Wales, Cowan in Western Australia, and Lilley in Queensland.

The Liberals’ Sarah Richards was narrowly ahead of Labor MP Susan Templeman by 23 votes in Macquarie, but trailing in Lilley and Cowan.

Postal and pre-poll results, which tend to favour the Coalition, are yet to be counted for the seats, which may yet boost the Coalition’s slim majority.

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Albanese told the ABC on Monday night Labor would need to reshape its policy offering and respect the sentiment of voters in Queensland, who swung to the Coalition and protest parties. He said if he emerged as the next Labor, his first stop would be Queensland.

“We have not sold the message well enough, I don’t think, that we are interested in jobs and economic growth as the priority, as well as the distribution of wealth in our society,” Albanese said on Monday night.

“Some of the policies – I think there are issues that need re-examining, and it’s up to the caucus. One of the things that I’m not going to do, if I’m elected as leader of the Labor party, is to make policy on the run.

“I’ll talk with the caucus, we’ll consult, and, on these issues, I think it’s very important that, in coming months, we have a listening exercise that I and other shadow ministers go out there, have meetings in towns and cities around Australia, and listen to the feedback from our party members, our supporters, and from those people who were disappointed with us as well.”