When Rishi Sunak arrives at the Conservative Party’s annual conference on Sunday, it will be his first as Britain’s prime minister. The question looming for many attendees in the cavernous venue in Manchester is whether it could also be his last.

Facing a general election within 16 months, Mr. Sunak has restored some stability after a tumultuous period for the Conservatives — who last year replaced two prime ministers within two months — but has failed to significantly narrow a big deficit in the polls against the opposition Labour Party.

All of this will play out against the backdrop of a cost-of-living squeeze, a health service in crisis and a continuing flow of asylum seekers arriving on small boats — all political poison for Mr. Sunak. Labor unrest has subsided somewhat, but rail workers have deliberately timed more strikes to coincide with the Conservatives’ gathering.

Faced with those mounting challenges, Mr. Sunak has recently come out fighting, weakening environmental commitments in the first of several anticipated announcements aimed at seizing the initiative.

The idea, analysts say, is to recast the prime minister as a conviction politician, in the process revealing the “real Rishi” Sunak.

“If you look at his personal ratings, they are as low as they’ve ever been, and the party is still between 15 to 20 points behind in the opinion polls, so clearly he had to do something,” said Tim Bale, a professor of politics at Queen Mary University of London. “Whether this is just, ‘For God’s sake, do something,’ rather than a thought-out plan, as they are trying to sell it, is more of a moot point.”

It is unclear whether this will be the last Conservative Party conference before the general election because Mr. Sunak can decide the date of the vote (though it must take place by January 2025). The most likely options are for the election to come in the summer of next year — before the 2024 Conservative Party conference — or in the fall, soon after.

Either way, this year’s meeting in Manchester, in northern England, comes at a delicate moment for Mr. Sunak, as he appears to have accepted that his strategy to date has left him staring at defeat.

“It’s his first conference as leader, and it’s very important in terms of defining himself,” said Robert Ford, a professor of political science at Manchester University.

With two of his predecessors as prime minister, Boris Johnson and Liz Truss, still a distracting presence, the objective will be “to keep those two off the newspaper front pages and their allies quiet, and to project an image of a party that is united and ready for the fight, rather than divided and hoping for the sweet release of electoral death,” Professor Ford added.

Until recently, Mr. Sunak’s strategy had been to focus on five objectives: halving inflation, growing the economy, reducing debt, cutting waiting lists for health procedures and stopping the arrival on British shores of asylum seekers in small boats.

Though the economic goals may be met in a technical sense this year, growth remains sluggish, prices are still rising fast and few Britons feel better off. The health care target is well off course, and the arrival of thousands of small boats remains a visible symbol of the failure of the Brexit referendum pledge to take back control of the nation’s frontiers.

Charles Lewington, a media chief for the Conservative Party during the 1990s, said that Mr. Sunak’s switch of gears would have happened anyway next year, but that it had been accelerated because of his failure to move the polls.

Given the electoral mountain Labour has to climb to win a majority after its heavy defeat in the 2019 general election, the Tories still have prospects of pulling off a surprise result, said Mr. Lewington, who is now executive chairman of Hanover Communications, a public affairs firm.

“They’ve realized that Labour’s change message is a big threat, so they are going to do what can they to position Rishi Sunak as the change candidate,” Mr. Lewington added.

But shifting gears has not been smooth. Mr. Sunak’s pledge to delay by five years a ban on the sale of gas and diesel cars and to lower targets for replacing gas boilers, seemed meant to set a dividing line between him and Labour’s leader, Keir Starmer, but also revealed divisions within the Conservative Party.

The new thinking follows the Conservatives’ surprise victory in July in a parliamentary election in northwestern London, where they campaigned against moves by the city’s Labour mayor to expand an air-quality initiative that raises fees for drivers of older, more polluting vehicles.

Mr. Sunak’s strongest argument now is that, unlike the Labour Party, he says he can meet climate goals without raising costs for hard-pressed Britons.

He also seems to be planning new measures to favor motorists and eyeing savings of public money by questioning the future of Britain’s proposed high-speed train link, known as HS2, which has already been scaled back as costs balloon. In recent days, Mr. Sunak has repeatedly refused to commit to continuing a leg of the project linking Birmingham, in central England, with Manchester, stoking speculation that it will be delayed or scrapped.

Were that to happen, however, it would walk back a signature promise made by Mr. Johnson to “level up” by spreading prosperity from the south to areas of the north and the Midlands that have missed out on economic growth in recent decades. Leveling up was meant to cement the support of former Labour voters in the north who defected to the Conservatives in 2019 and powered Mr. Johnson’s landslide election victory.

Awkwardly, the HS2 debate remains unresolved as the Conservatives meet in Manchester, one of the largest cities in the north of England and the place that perhaps stands to benefit most from the project.

Other ideas being floated include the abolition of inheritance tax, a policy that has long been favored on the right of the Conservative Party. But the optics of that would be difficult for Mr. Sunak because it would benefit wealthy Britons — and the prime minister is among the wealthiest.

Professor Ford believes that the new announcements may be intended primarily to rally Conservative Party activists and lawmakers and to please the country’s right-wing media, which has a powerful influence over them.

The change also makes sense for Mr. Sunak, he said, not only because the prime minister needs to gamble, given his poll numbers, but also because he will not have to deliver on most new commitments because time is too short before the general election.

But the risk is that when the “real Rishi” is revealed to voters, many may not like what they see.

Moderate Conservatives in the south of England initially warmed to him last year, after he brought stability following Ms. Truss’s disastrous 44 days in Downing Street.

Mr. Sunak, who has a penthouse apartment in Santa Monica, Calif., “gave off this Californian cosmopolitan vibe,” Professor Ford said, and therefore many college-educated metropolitan voters “imagined him to be the kind of politician he isn’t.”

“In fact,” Professor Ford added, “he’s very right-wing on economic issues, he’s socially conservative.”

That social conservatism could be popular in parts of the north and the Midlands, Professor Ford said, but “that’s not what they are prioritizing at the moment.”

Rather than Brexit, and the immigration and culture war issues that dominated past elections, Professor Ford said that people in those areas were talking about the cost of living, the economy, the health service.

“So,” he added, “it’s not clear what the electoral market for the ‘real Rishi’ is.”