But she says that will only be the case if MPs are willing to approve the withdrawal agreement bill in the House of Commons in the first week of June.
When Mr Snow remarked: "that puts it pretty succinctly" the Tory MP responded: "You've asked for a succinct answer and I have given it to you".
She now believes the new proposal, which she described as a "bold offer" in a televised address, will scale through, following an extended reprieve she got from the European Union earlier this year.
In a sign that the British public has already moved on, numerous questions May fielded during Tuesday's news conference had to do with when she will resign and what might happen after that. He later told reporters there was no chance of getting even part of a Brexit deal ratified by the end of July.
May wants to get her withdrawal deal, agreed with the European Union last November, through parliament so she can leave office, as promised, having at least finalised the first part of Britain's departure and prevented a "no deal" Brexit, an abrupt departure that many businesses fear will create an economic shock.
Did the prime minister just make it worse?
"Boris wrote in his column repeatedly that Mrs May's new treaty was vassalage - that we'd become a slave state - and I rather agreed with that analysis, even if his language was more colourful than perhaps what I would use".
Corbyn said Friday that "without significant changes, we will continue to oppose the government's deal, as we do not believe it safeguards jobs, living standards and manufacturing industry in Britain".
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But after three previous attempts to get her deal through the Commons went down to hefty defeats, many Tory MPs are sceptical that her fourth will fare any better.
Mrs May also said it is not possible to replace the Irish backstop.
Theresa May's so-called "new deal" is meant to appeal to MPs on both sides of the House and both sides of the Brexit divide.
She said the vote would be contained in the new Withdrawal Agreement Bill, as she warned that a failure to reach an agreement on Brexit would lead to a "nightmare future of permanently polarised politics".
The government will also introduce a new Workers' Rights Bill to "ensure United Kingdom workers enjoy rights that are every bit as good as, or better than, those provided for by European Union rules". She said she recognized "the genuine and honest strength of feeling" on the referendum issue.
The Prime Minister Theresa May has set out a 10-point compromise package ahead of what she indicated would be her final attempt to secure approval for a deal which has already been rejected three times by MPs.
May hopes that with those additional voting opportunities and some tweaks to her deal - including pledges on environmental protections and workers' rights - she can win over enough lawmakers to get it over the line.
"This deal lays the groundwork and settles numerous core issues, but in the years ahead Parliament will be able to debate, decide and refine the exact nature of our relationship with the EU".