Sunak is trying to secure the backing of all sides in Northern Ireland and eurosceptic lawmakers so he can reset relations with the EU - and the United States - without angering politicians in his own party and in Belfast who are most wedded to Britain's 2020 departure from the EU.
His deal seeks to resolve the tensions caused by the Northern Ireland protocol, a complex agreement which set the trading rules for the British-governed region that London agreed before it left the EU, but now says are unworkable.
In order to keep open the politically sensitive border with EU-member Ireland, Northern Ireland remained in the EU single market for goods, raising the prospect it would slowly diverge from the rest of the United Kingdom, fuelling fears in unionist communities.
Sunak said his agreement, the Windsor Framework, would bolster the union, scrap rules that affected everything from the import of sausages to sandwiches, and give lawmakers on the ground a greater say over the rules and regulations they take from EU headquarters in Brussels.
The success of the deal is likely to hinge on whether it convinces the Democratic Unionist Party (DUP) to end its boycott of Northern Ireland's power-sharing arrangements. These were central to the 1998 peace deal which mostly ended three decades of sectarian and political violence in Northern Ireland.
Sunak said he wanted to explain the details to the different communities in Northern Ireland, and accepts that will take time. "I'm also very keen, we've not been shy about saying, that the people of Northern Ireland need and deserve their government," he told reporters.
DUP leader Jeffrey Donaldson said his first reading of the deal suggested it would give the Stormont regional assembly the power to reject EU rules it did not want, providing some reassurance on their key concern of sovereignty.
But he said the party is likely to take time before it comes to a conclusion, while members of the European Research Group, which brings together hardline pro-Brexit Conservative lawmakers, will work with lawyers to examine the details before giving a verdict in a process that could take two weeks.
Sunak later told a meeting of his lawmakers in parliament that the public are fed up with the constant disputes over Brexit and said they should back his deal or risk losing the trust of voters, according to lawmakers who attended.
The prime minister said the DUP deserved "time and space" to consider their response.
Steve Baker, the junior Northern Ireland minister, said after the meeting the deal will win broad parliamentary support because his party realises this is the best Britain can get from the EU and there is "relief" at what has been agreed.
The new deal is a high risk gamble by Sunak, just four months into the job. Most British newspapers lauded his achievement in getting the EU to soften its stance, while saying success would only come from the resumption of the power-sharing assembly in Northern Ireland.
A victory would strengthen Sunak's hold over his Conservative Party and enable him to move past the thorniest issue on his agenda as he seeks to catch up with the opposition Labour Party, now well ahead in opinion polls, before a national election expected in 2024.
It could also lead to deeper cooperation between Britain and the EU in other areas such as scientific research, the regulation of financial services and the movement of small boats carrying migrants in the channel.
But any serious rebellion by the eurosceptic wing of his party would revive the ideological divisions that have at times paralysed the government since the narrow referendum vote to leave the EU in 2016.
Officials in London and Belfast say Sunak was motivated to act before the 25-year anniversary of the Good Friday Agreement, which could entail a visit from U.S. President Joe Biden.
Biden welcomed the deal on Monday, while his Secretary of State, Antony Blinken, hailed the "opportunity, certainty, and stability brought about by the agreement".