Mr Sunak stole a small step on Ms Truss by telling the News Letter he would push through the Bill in its current form and not allow it to be watered down by the Lords.
The former Chancellor is grappling with the perception that Reformed Remainer Ms Truss is tougher than him on protocol despite his impeccable Brexiteer credentials.
The Treasury has rejected plans to trigger Article 16 of the protocol, a clause allowing certain parts of the treaty not to be applied, for fear of starting a trade war with Brussels.
But both Mr Sunak and Ms Truss are continuity candidates on Brexit and Northern Ireland, with neither promising a new approach to Mr Johnson’s policy.
So far, this policy has failed to eliminate the burdensome border controls introduced by a treaty the government negotiated and signed.
This brought the EU and UK to the point of threatening each other with legal action, tariffs and, at one point, on the brink of a trade war over sausages.
It has angered Joe Biden in Washington, dashed dim hopes of a UK-US trade deal and strained relations with Dublin.
Bill fails to convince the DUP to drop the boycott
Clearly, the bill failed in its main objective of convincing the DUP to abandon its boycott of the Northern Ireland Assembly and enter into power-sharing with Sinn Féin.
Sinn Fein became Northern Ireland’s largest party for the first time in the country’s history after the May 5 election, which was seen by many as a de facto referendum on the Protocol.
The DUP will not form a devolved government until the Protocol is removed or replaced.
Meanwhile, Stormont is powerless to tackle the UK’s longest NHS waiting lists or the cost of living crisis.
Sinn Fein, which is pushing for a reunification referendum within the next decade, is quick to point this out.
Mr Sunak and Ms Truss will flex their muscles in Brussels during the roundups after a campaign that has so far prompted little debate over protocol.
Tough talks may play well with the DUP, but it will further alienate the rest of Northern Ireland’s political parties, who represent a pro-protocol majority after the Stormont election.
But the target audience for both candidates is not Northern Ireland voters, who have primarily backed Remain, or even EU power brokers.
It is the Conservative members of the UK who will elect Boris Johnson’s successor as Prime Minister.
Both the UK and the EU are guilty of arming Northern Ireland since Brexit.
The country is again used as political football.
One day, if a referendum on reunification is held, the Northern Irish may back down.