Boris Johnson is edging towards the parliamentary numbers needed to pass a Brexit deal after more hardline Eurosceptics and pro-deal Labour MPs indicated they could back a new agreement made with the EU.

The prime minister will need to win over almost all the 28 Tory “Spartans” who held out against Theresa May’s deal if he manages to bring an agreement back from Brussels, as well as either the Democratic Unionist party or a chunk of Labour backbenchers.

There are signs that Tory Eurosceptics are moving towards backing an agreement, partly because they fear that Labour could try to push for a second referendum instead of an election.

Lee Rowley, a Conservative MP who voted down May’s deal three times, gave a loyal address after the Queens speech saying he had shifted his position and his view was that parliament must get Brexit done.

“We are in a hard place and all of us, whatever bench or chair we sit in, are responsible for where we end up,” he said. “In the last few days, there is at least hope that this toxic and crippling fog, which we have created, might just be lifting as the prime minister sketches the outline of a way forward – and I speak as someone who has been robust in my review of previous proposals, but the House must surely see that we have debated long enough.

“This is a moment for decision and we were elected to make decisions. If there is light at the end of the tunnel later this week, and heaven knows I hope there will be, we have a fundamental responsibility in this place to try and resolve this most vexed of problems and allow our despairing country to move on. For the health of our democracy and to restore faith in this most venerable of institutions, in my view we simply must get Brexit done.”

Several of the “Spartans” are now on Johnson’s payroll with government jobs, such as Priti Patel, the home secretary, who is understood to be prepared to support whatever the prime minister brings back from Brussels.

Another of the Tories who voted against May’s deal told the Guardian that he would be reassured if the DUP backed the prime minister but could end up voting for it regardless. “Whatever the prime minister comes back with, I’m going to have a very long and pragmatic look at it. I think a second referendum would be a disaster and I don’t think our democracy could stand that,” he said.

In a video for the Stand Up for Brexit campaign, Steve Baker, one of the most fervent Eurosceptics, sounded positive about the potential for a deal he could vote for. “Most of us, including me, overwhelmingly want a deal … we have got to be capable of getting there through a withdrawal agreement,” he said.

“The problem with the previous withdrawal agreement is it was capable of leaving us trapped in the orbit of the EU, a declining satellite of the EU with no benefits from leaving. Boris has had a dramatic shift towards a free trade agreement that would leave us a self-governing nation … So now really, the devil is in the detail … I am really looking forward to being able to vote for a tolerable deal but, until we get the text, I cannot tell you what we are going to do.”

Others have sounded more sceptical, such as the former Northern Ireland secretary Owen Paterson, who criticised the EU for demanding more and more concessions.

Several DUP MPs sound unconvinced, but Johnson may not need their votes if he can secure enough support among Labour MPs and retain the support of his own party plus most former Tories who want a deal rather than a second referendum.

About 18 Labour MPs signed a letter last week urging the EU to work day and night towards a deal, saying their votes would be decisive in whether it got through parliament. Melanie Onn, a Labour backbencher, has said she would support a “reasonable deal” and wrote on her Facebook page on Monday: “A no-deal Brexit would hinder not help the town and people of Grimsby. I will vote for a deal in the best interests of Great Grimsby to ensure a no-deal Brexit is prevented.”

Others who have indicated they could now be prepared to vote for a deal with the right reassurances on Northern Ireland, workers’ rights and environmental protections include Stephen Kinnock, Gareth Snell and Ruth Smeeth. Gloria De Piero has said she will look at any new deal seriously.

However, they are likely to face fierce opposition from some of their pro-remain Labour colleagues and possible calls for the whip to be withdrawn.

It is likely to become clear within the next few days whether it will be possible for a deal to be done at Thursday’s European summit and it could drag on until next week. The government will have to table a motion in parliament by Wednesday if it wants to convene MPs for a Saturday sitting to debate any agreement.

A Downing Street spokesman would not confirm whether it would hold the first Saturday sitting since the Falklands war if Brussels talks failed to find an agreement. “The point here is, for example if a deal is done at European council, a Saturday sitting would certainly allow you to start the process of getting the deal through,” he said.