A number of major names have gone public with their endorsement of Liz Truss over the past fortnight, with announcements carefully timed by her campaign strategists at opportune moments to seize headlines.

But to maintain momentum over the coming weeks as new policies dry up, the foreign secretary’s team want to go one further by flipping those who have already declared support for her Conservative leadership rival, Rishi Sunak.

They hope to further grind down his camp’s already flagging morale by convincing MPs to back a winner, pointing to Truss’s runaway lead in numerous opinion polls.

But the more her chances of becoming prime minister grow, the less reward there is for those who jump ship and are accused of rank opportunism.

The most coveted endorsements are those of other leadership contenders, given the attention they attract and the fact they often bring their allies along, too.

Penny Mordaunt stole the show at the second hustings in Exeter by striding up to the stage to introduce and back Truss. However, some of her supporters felt betrayed and did not follow suit, given that they blamed the foreign secretary’s team for a string of smears that left Mordaunt edged out of the members’ ballot by potentially just four MPs’ votes.

Earlier in the contest, Tom Tugendhat was waiting with open arms to welcome Truss at a campaign event held at an army base. Weeks ago a simple backbencher but now regarded as a heavyweight for coming fifth in the Tory leadership race, his support was crucial in bringing along other “one nation” MPs.

Another helpful endorsement for Truss came in the form of Sajid Javid, who, though he had to pull out of the race in the early stages after failing to garner enough nominations, has served in several cabinet posts. The sting in his snubbing of Sunak, his friend and former protege at the Treasury, left Truss’s team rubbing their hands with glee.

Having scooped up most of the cabinet – the defence secretary, Ben Wallace; the business secretary, Kwasi Kwarteng and arch Boris Johnson loyalists such as Nadine Dorries and Jacob Rees-Mogg – there is still one former leadership contender who has yet to give her endorsement.

Kemi Badenoch, tipped as a rising star by the Tory right, has been wooed but so far has kept her powder dry.

A Truss ally complained that if Badenoch did not “go over the top, it might determine [whether] she gets a job in the cabinet”. They said other MPs had had to endure media rounds, taking flak for Truss on her behalf and added: “You’d be aggrieved if someone who couldn’t be bothered got parachuted right to the top.”

Sunak has failed to win any major new endorsements since all seven of his cabinet backers emerged early at the start of the campaign. His latest backers have mostly included the old guard – former Tory leaders like William Hague and Michael Howard, as well as Thatcher-era cabinet ministers including her chancellor, Nigel Lawson.

Given the way the contest is shaping up, several declared Sunak supporters said they had been quietly encouraged by Truss’s team to switch sides.

James Evans, a Conservative member of the Senedd in Wales, declared after this week’s hustings in Cardiff that he had initially backed Sunak “but as this has gone on there is only one person to unite the country and the party and that is Liz Truss”.

Pictured beaming next to her in the post announcing his decision, Evans had tweeted no previous expressions of support for Sunak. And an ally of the former chancellor insisted he had “never come out for us”.

Another source on Sunak’s team accused Truss of “desperately” trying to hoover up his supporters. “That’s the only way she’ll keep momentum up, and it’ll be toxic for us,” they sighed. “It is sucking momentum.”

“If anybody does switch, it won’t be because they’ve changed their mind, it’ll be because they’ve lost their nerve and got in a flap,” a third said.

Truss’s campaign argue that they are simply trying to prepare for the end of the contest, which has prompted damaging blue-on-blue attacks.

About two dozen Truss supporters will sign a letter published later this week stressing the need for the party to unite, as Sunak’s team grow increasingly exasperated and seek to land more blows on her in an attempt to avoid him looking like a loser-in-waiting.

One MP who has refused to endorse either candidate predicted there would soon be “rats deserting the sinking ship”.

But even if Truss does manage to score some more points over Sunak by flipping supporters, she will inherit a restive party.

“She might have the associations on board, but she’ll suffer the same fate as [former Labour leader] Jeremy Corbyn and not be able to command control of the parliamentary party,” warned another Tory source, who is yet to declare. “She might win this battle, but not the war.”