It was only the first day of federal parliament for 2021 on Tuesday, but all eyes in Canberra are already on the next election – even if the Prime Minister, at least publicly, is saying it could be some way off.

An unprecedented 2020 saw all the usual rules of politics thrown out the window, and (most of) the normal petty parliamentary bickering temporarily shelved.

Tuesday saw ‘business as usual’ largely recommence, with a near-full chamber of politicians, a very shouty Question Time, and yet more debates about climate change and industrial relations tearing apart Parliament House.

But despite Scott Morrison’s continual assertions that he is a “full-termer” and doesn’t plan to call an election before the May 2022 deadline, Tuesday also saw the barest hints that both major parties were gearing up for a poll this year.

Both Mr Morrison and his Liberal deputy, Treasurer Josh Frydenberg, used the first Coalition partyroom meeting of 2021 to counsel their colleagues that the next election is not yet won.

Scott Morrison told colleagues to stay focused. Photo: AAP

“It is important not to believe commentators who say that we have already got the next election in the bag,” Mr Frydenberg said.

“We must continue to focus on the job we’re doing.”

Mr Morrison, after stressing in multiple media interviews in recent weeks that he didn’t plan to call an election this year, also told his team to keep working.

“No matter what else is happening around you, remain coordinated and together as a team – that’s the approach we all need to bring,” Mr Morrison said.

According to sources present at the private partyroom meeting, the PM told his members to “keep your eyes in the boat” – apparently a phrase borrowed from his high school rowing coach.

• Related: Michael Pascoe: When PM calls his early election, that’s when we should really start to worry

The Treasurer spoke of past surprise election results – in the early 2000s when former Liberal leader John Howard won against the odds, and in 2019 when former Labor leader Bill Shorten lost the so-called ‘unloseable election’ – as cautionary tales about losing focus.

Privately, Coalition members are already looking toward an election in 2021. One senior Coalition source told The New Daily the party was looking at the example of Mr Shorten, defeated by Mr Morrison at the last election after consistently leading in polls, as a warning about complacency.

“We won’t take our foot off the pedal,” they said.

Even as the PM himself talks down whisperings of a 2021 poll, it’s clear that senior Coalition members are aware many others do think an election is on before the year is out.

Labor’s new email header – a small but symbolic change.

In the Labor camp, a more subtle but no less symbolic change – the party has updated the email header in messages sent to journalists, to display their new campaign slogan: “On your side”.

Labor’s campaign committee is now starting to meet and plan an election strategy. The committee has not met for a decade, according to senior Labor sources, who said the party had not used that formal structure for the past few campaigns.

The committee structure, which brings in a wider variety of party and union officials from across the country to discuss policy and tactics, was described by senior sources as a more consultative process which may have been of benefit in recent unsuccessful Labor campaigns.

Monday’s NewsPoll result had Labor at 50-50 with the Coalition, while Tuesday’s Essential poll actually had the opposition ahead.

Opposition leader Anthony Albanese says he will be ready for an election, whenever it comes, but even despite the better-than-expected polling numbers, mutterings from a small number of unhappy Labor members mean his leadership is again being questioned.

Mr Albanese’s supporters from the left faction of the party are adamant he is going nowhere, and commands the support of the majority of his fellow MPs and an even larger percentage of ordinary party members.

#Essential Poll Federal 2 Party Preferred: L/NP 44 (-4 since October) ALP 47 (+2) Undecided 8 (0)
(Undecided excluded: L/NP 48 (-2) ALP 52 (+2)) #auspol

— GhostWhoVotes (@GhostWhoVotes) February 2, 2021

But some among Labor’s right flank believe Mr Albanese’s strategy may not win them an election, with whisperings about other frontbenchers like Tanya Plibersek, Jim Chalmers, Richard Marles or Chris Bowen. Some point to a possible Plibersek-Chalmers ticket.

TND has spoken to several right-faction Labor sources who say they are actively investigating how they could force the leadership question to a head – either through a partyroom vote, or encouraging Mr Albanese to resign.

The second option would be near-impossible, considering Mr Albanese’s staunch belief he is the party’s best option, and the neck-and-neck poll numbers, which Mr Albanese stresses are at least a three-point boost from the 2019 poll.

That would leave the forcing of a party vote, but leadership rules instituted by former PM Kevin Rudd mean that a leadership vote could only be triggered by a majority of the partyroom; again, a near-impossible ask at this stage.

Mr Albanese and Mr Shorten. Photo: AAP

Perhaps not coincidentally, rogue Labor backbencher Joel Fitzgibbon – who quit the shadow ministry after a dispute with Mr Albanese – has called in recent weeks for the party to overhaul its leadership rules.

The government took aim at Labor’s internal ructions on Tuesday. In a Question Time answer boasting of the Coalition’s jobs record, Mr Frydenberg claimed the opposition had “spent their summer trying to save just one job” – Mr Albanese’s.

Mr Morrison joked Labor had “become a fight club, not an opposition, and cannot agree with itself.”

In their own partyroom, the opposition had pledged to formally oppose the government’s industrial relations omnibus bill. The Opposition had previously signalled an intention to oppose it, if controversial changes to sideline the Better Off Overall Test (BOOT) were not removed, but Mr Albanese’s party will now officially vote against it.

It sets up another almighty fight on IR reform, with the union movement already having threatened a WorkChoices-style campaign of strikes and industrial action to oppose the legislation.

Election rumours, leadership rumblings, and a stoush on IR – it’s back to business as usual in Canberra. Bring on the rest of 2021.