Labour’s two leadership challengers, Angela Eagle and Owen Smith, were neck-and-neck in nominations from MPs in the first day of voting but were believed to have agreed that only one will face Jeremy Corbyn on the ballot paper.

Allies of Eagle dismissed claims by Smith’s camp that she was haemorrhaging support to the MP for Pontypridd, saying the number of nominations for each were roughly equal after a strong performance at the hustings of the parliamentary Labour party. It was clear Labour MPs wanted a single challenger to take on Corbyn, one Eagle supporter said.

Eagle and Smith want to avoid splitting the anti-Corbyn vote, as a poll of Labour members published on Monday night showed the leader was on course to easily defeat either challenger.An idea has been mooted that the less-favoured challenger could form part of a joint ticket as shadow chancellor or a similarly senior role.

Smith, the former shadow pensions secretary, has already said he will back down if he gets fewer nominations in a process that runs until 5pm on Wednesday and Eagle’s supporters hinted she would do the same.

Eagle will not step aside if she is behind in nominations by 5pm on Tuesday, the halfway point when the party will announce how many supporters each candidate has. “It’s like someone dropping out at 2am on election night. It won’t happen,” one source said.

Caerphilly MP Wayne David, who suggested at Smith’s launch last week that the former shadow business secretary should give way to his candidate, had signed Eagle’s original nomination papers that cleared the way for a challenge to Corbyn, the source added.

At a hustings, when Yvette Cooper asked the two challengers if they were prepared to step aside if they won lower levels of support from MPs, Eagle said she would not make “backroom deals”.

However, one Labour MP told the Guardian that they had since given their nomination to Eagle after the former shadow business secretary gave assurances she would stand aside if Smith gained more supporters.

Hilary Benn, whose dismissal as shadow foreign secretary in June was the catalyst for a vote of no confidence in Corbyn from fellow Labour MPs, said on Tuesday his party was “in an unhappy and a difficult place”. However, Benn insisted Labour would not split, even if party members re-elected Corbyn.

Speaking on BBC Radio 4’s Today programme, Benn, a supporter of Eagle, said there was “a strong view in the parliamentary Labour party that there should only be one challenger”.

“I think that would be preferable, it’s the view of many Labour MPs,” he said. “But Angela and Owen would both make great leaders of the Labour party. What we have to do is to get out of the situation that we’re in. Jeremy has done a great deal for the party – he’s changed politics, he’s brought his values, he’s made a huge contribution and will continue to do so. The problem is that the clear majority of his colleagues in parliament don’t think that he is a leader.”

Even if a single challenger emerges, they face an uphill challenge in September’s members’ vote, with a YouGov poll for the Times saying that Corbyn would defeat both Smith and Eagle by more than 20 percentage points.

The survey, carried out between Friday and Monday, found that 44% of Labour members said they would definitely vote for Corbyn, eight percentage points higher than a poll two weeks ago, with a further 13% saying they would probably vote for him.

In a hypothetical vote against Eagle, Corbyn would win by 58% to 34%, the poll said, and by 56% to 34% against Smith.

The situation is complicated by uncertainty over voting rules after Labour’s national executive committee decided last week to allow Corbyn on to the ballot even if, as expected, he fails to gain the support of the 51 MPs or MEPs theoretically needed. However, it also changed the eligibility rules for member voting.

The NEC said only those who had joined Labour six months or more ago could vote, excluding the 130,000 or so people who have signed up since the EU referendum. However, people can still pay £25 by Wednesday afternoon to sign up as a registered supporter and vote.

During Tuesday’s meeting, NEC members clashed again over the high cost for registered supporters and the short deadline to sign up, one source said. It is unclear if it is possible under Labour party rules to overturn that decision.

The NEC is facing two legal challenges to its decisions. A Labour donor, Michael Foster, is seeking to overturn the ruling that Corbyn can automatically stand. He is due to lodge the high court case on Thursday, with Corbyn seeking to apply to be a party to the case, meaning his lawyers can argue in court.

Separately, a leading London law firm is understood to be mounting a class action on behalf of 2,000 Labour members who joined the party in the past six months and claim its stated conditions said they would be able to vote in any leadership poll.

Amid the confusion, Benn said on Tuesday that it was a tough time for the party, but that Corbyn had to go.

He told the Today programme: “We’re in an unhappy and a difficult place at the moment, and I trust that Labour party members, when they look at the situation we are in, will realise that for all Jeremy’s qualities, if he doesn’t have the confidence of the people he’s meant to be leading in parliament, how can he credibly turn to the people of Britain and say, elect me as your prime minister?”

While Benn said he would not support Corbyn if the Labour leader was re-elected, he played down the idea of the parliamentary party somehow separating: “The Labour party is not going to split. Let’s be absolutely clear about this.”