Theresa May has warned Conservative rebels pushing for a leadership contest that they could delay Brexit or even stop it.
Speaking to Sky's Sophy Ridge on Sunday, Mrs May said a new Conservative Party leader would not make negotiations with the EU any easier - after days of speculation over a leadership election.
Sir Graham Brady, the chairman of the backbench 1922 committee, told Sky News that if he does receive the 48 letters required to force a confidence vote in the prime minister, he would act "expeditiously" in announcing it - indicating there are not enough to do so.
"It's a nonsense to suggest anybody would hang around," he said.
It comes as Mrs May fights to get her cabinet, parliament and the country to back the Brexit agreement she has struck with Brussels.
Mrs May said she was going back to Brussels over the next seven days and was determined to deliver the Brexit that was best for country, but would not be swayed by talk of leadership challenges.
She told Sophy Ridge on Sunday: "A change of leadership at this point isn't going to make the negotiations any easier and it's not going to change the parliamentary arithmetic.
"What it will do is mean there is a delay to those negotiations and that's a risk that Brexit gets delayed or frustrated.
"This isn't about me. This is about the national interest. The next seven days are critical."
Mrs May had earlier said she believed the 48-letter trigger point had not been reached, despite two cabinet resignations last week and numerous pro-Brexit MPs openly saying they would not accept the EU agreement.
The PM reiterated that the much-discussed backstop plan contained within the agreement did not mean the UK could be locked into an arrangement that was not in its interest.
When Sophy Ridge asked: "Is the backstop like the 'Hotel California', you can never leave?", Mrs May said: "You can leave."
She compared the backstop to taking out an insurance policy, saying people wouldn't want the insurance company to be able to "pull the plug" and leave someone unprotected.
It is a "backstop we never intend to use", she said, adding: "Were it to have to be used, both sides can review it".
When she visits Brussels, she said, she will talk to EU Commission president Jean-Claude Juncker.
UK negotiators are already visiting the EU's HQ, as they move on to what Mrs May called the next phase of the negotiations - the "future relationship".
"There is more negotiation taking place. Nothing is agreed until everything is agreed. We've agreed the withdrawal agreement in principle. It goes alongside the future relationship," she said.
When asked about how she felt personally about the comments she had heard about herself over the last few weeks, she replied: "Who are we here for? The important thing is that we're here for our constituents and as prime minister I'm here for the people of this country."
Sir Graham later suggested the 48 letter threshold had not been reached, telling Sky News that announcing it had was "intended to be a very expeditious thing".
"It's a nonsense for people to suggest that anyone would hang around," he said.
Earlier, Jeremy Corbyn told Sky News a second EU referendum was an "option for the future, but not an option for today".
Quizzed by Sky's Sophy Ridge, Labour's leader said he didn't know what question would feature in a referendum.
Asked how he would vote today if he could, he said: "I don't know."
Mr Corbyn also admitted he had not read all of Theresa May's Brexit agreement, saying "I've read a lot of it".
He added that he had read many of the summaries and analyses.
Much of the reason he said he wouldn't support Theresa May's deal was because it was "vague" and did not say enough about workers rights and environmental protections.
He suggested he would support a deal like that struck by the prime minister if it addressed those concerns.
Leader of the Liberal Democrats Sir Vince Cable responded by accusing Mr Corbyn of "wanting Brexit to happen" and "helping" the prime minister deliver it for "short term political calculations".
He added that the choice was rapidly becoming 'no deal and no Brexit' - and that stopping the UK's exit from the EU was becoming "a probability".
And the DUP's Westminster leader Nigel Dodds piled pressure on Mrs May to drop her draft Brexit deal, saying it was "clear that it is time to work for a better deal which does not undermine the integrity of the United Kingdom" .